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Singular Limits of Voigt Models in Fluid Dynamics

Michele Coti Zelati, Ciprian G. Gal
2015 Journal of Mathematical Fluid Mechanics  

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2014 pre-print arXiv:1408.3497v1 fatcat:w7ozu5nma5gxfpjys6sqiose3u

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2014 accepted
arXiv:1408.3497v2 fatcat:ljlfha57qzhx5ljy4gks4dtqy4
Finally, we also prove convergence of the (strong) global attractor of the 3D Navier-Stokes-Voigt model to the (weak) global attractor of the 3D Navier-Stokes equation.  ...  We investigate the long-term behavior, as a certain regularization parameter vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic incompressible fluid.  ...  Titi for being a continuous source of inspiration. The work of the first author was also supported in part by the NSF Grant DMS 1206438, and by the Research Fund of Indiana University.  ... 
doi:10.1007/s00021-015-0201-1 fatcat:dtspu7k57zemfpdwofiaunmcci
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Michele Coti Zelati, Ciprian G. Gal. "Singular Limits of Voigt Models in Fluid Dynamics." Journal of Mathematical Fluid Mechanics 17.2 (2015) 233-259

Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains

Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang
2019 Discrete and continuous dynamical systems. Series B  

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This article focuses on the optimal regularity and long-time dynamics of solutions of a Navier-Stoke-Voigt equation with non-autonomous body forces in non-smooth domains.  ...  to seek the uniform attractors for 2D non-autonomous NS equation(see [24]).  ...  All the authors thank the referees by their comments and guidances, leading to improvements of this paper for publishing. LONG-TIME DYNAMICS FOR A NON-AUTONOMOUS NAVIER-STOKES-VOIGT EQU. 385  ... 
doi:10.3934/dcdsb.2018084 fatcat:eqwv4bwdtvcfhdtxmq4v2jhjqm
Citation

Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. "Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains." Discrete and continuous dynamical systems. Series B 24.1 (2019) 363-386

Pullback attractors for three-dimensional Navier-Stokes-Voigt equations with delays

Haiyan Li, Yuming Qin
2013 Boundary Value Problems  

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Our aim in this paper is to study the existence of pullback attractors for the 3D Navier-Stokes-Voigt equations with delays.  ...  Since the solution of the model is not unique, which is caused by the continuity assumption, we establish the existence of pullback attractors for our problem by using the theory of multi-valued dynamical  ...  Gal and Medjo [] proved the existence of uniform global attractors for a Navier-Stokes-Voigt model with memory.  ... 
doi:10.1186/1687-2770-2013-191 fatcat:mk2paeb355akvkw22oeksuknsa
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Haiyan Li, Yuming Qin. "Pullback attractors for three-dimensional Navier-Stokes-Voigt equations with delays." Boundary Value Problems (2013) 191

Existence and invariant measure of pullback attractors for 3D Navier-Stokes-Voigt equations with delay [article]

Yuming Qin, Huite Jiang
2024 arXiv   pre-print

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In this paper, we study the long-time dynamics of 3D non-autonomous Navier-Stokes-Voigt(NSV) equations with delay.  ...  Furthermore, we verify the regularity of pullback attractors by the method in [14, 43, 47] and there exists a unique family of Borel invariant probability measures which is supported by the pullback attractors  ...  Navier-Stokes-Voigt systems have been proposed as regularizations of the 3D Navier-Stokes equation for the purpose of direct numerical simulation in both autonomous and non-autonomous cases (cf. [4, 5,  ... 
arXiv:2402.17347v1 fatcat:xpdhudugvreppaqp6hytevzyja
Citation

Yuming Qin, Huite Jiang. "Existence and invariant measure of pullback attractors for 3D Navier-Stokes-Voigt equations with delay." arXiv (2024)

Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations

T. Caraballo, 1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012-Sevilla, SPAIN, A. M. Márquez-Durán, 2 Departamento de Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, Ctra. de Utrera, Km. 1, 41013-Sevilla, SPAIN
2020 AIMS Mathematics  

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In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified formulation.  ...  for the exponential stability in a general case which, in particular, for a situation of variable delay, it only requires measurability of the variable delay function.  ...  Recently, Navier-Stokes-Voigt systems have been proposed (see [4] ) as regularizations of the 3D-Navier-Stokes equation for the purpose of direct numerical simulation (see also [1-3, 14, 21, 23, 31]  ... 
doi:10.3934/math.2020351 fatcat:q3cho4ppwfarrexdogeu553vlq
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Citation

T. Caraballo, 1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012-Sevilla, SPAIN, A. M. Márquez-Durán, 2 Departamento de Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, Ctra. de Utrera, Km. 1, 41013-Sevilla, SPAIN. "Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations." AIMS Mathematics 5.6 (2020) 5470-5494

Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with 'fading memory'

Manil T. Mohan, ,Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India
2019 Evolution Equations and Control Theory  

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We investigate the long-term dynamics of such viscoelastic fluid flow equations with "fading memory" (non-autonomous).  ...  We also show the existence of an exponential attractor for the semigroup associated with the transformed (equivalent) autonomous Kelvin-Voigt fluid flow equations with "fading memory".  ...  Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110).  ... 
doi:10.3934/eect.2020105 fatcat:ko5guilr3jecbis3roguo6ggvq
Citation

Manil T. Mohan, ,Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India. "Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with 'fading memory'." Evolution Equations and Control Theory 0.0 (2019) 0-0

Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations

Manil T. Mohan, ,Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India
2017 Discrete and continuous dynamical systems. Series B  

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Furthermore, the case of α = 0 and β > 0 can be considered as the Navier-Stokes-Voigt equations with damping, or the tamed Navier-Stokes-Voigt equations.  ...  The global attractors of 2D and 3D Navier-Stokes-Voight equations and related problems are discussed in [9, 23] , etc.  ...  Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110) and Indian Institute of Technology  ... 
doi:10.3934/dcdsb.2020067 fatcat:xjezd5ibwbhnreoc7on5usxium
Citation

Manil T. Mohan, ,Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India. "Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations." Discrete and continuous dynamical systems. Series B 22.11 (2017) 0-0

Pullback attractors for three-dimensional non-autonomous Navier–Stokes–Voigt equations

Julia García-Luengo, Pedro Marín-Rubio, José Real
2012 Nonlinearity  

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In this paper we consider a non-autonomous Navier-Stokes-Voigt model, to which a continuous process can be associated.  ...  Our results simplify -and in some aspects generalize-some of those obtained previously for the autonomous and non-autonomous cases, since for example in Section 4, regularity is not required for the boundary  ...  -L. is a fellow of Programa de FPU del Ministerio de Educación (SPAIN). The authors would like to thank the referees for their helpful comments and suggestions.  ... 
doi:10.1088/0951-7715/25/4/905 fatcat:qpyg5s6esffjfon3kfvfeomnwq
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Julia García-Luengo, Pedro Marín-Rubio, José Real. "Pullback attractors for three-dimensional non-autonomous Navier–Stokes–Voigt equations." Nonlinearity 25.4 (2012) 905-930

Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain

Xin-Guang Yang and Shubin Wang sci
2019 Journal of Partial Differential Equations  

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This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like  ...  Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh's friction and Navier-Stokes-Voigt flow, but invalid for three dimension.  ...  [1] extended to non-smooth domains of 2D Navier-Stokes equation by critically invoking estimates of the Stokes problem.  ... 
doi:10.4208/jpde.v32.n1.6 fatcat:qxfjkbxqyzbzhaypx4fnwyj3qa
Citation

Xin-Guang Yang and Shubin Wang sci. "Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain." Journal of Partial Differential Equations 32.1 (2019) 77-92

Dynamics of stochastic three dimensional Navier–Stokes–Voigt equations on unbounded domains

Quoc Bao Tang
2014 Journal of Mathematical Analysis and Applications  

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The aim of this paper is to study the long time behavior of the following stochastic 3D Navier-Stokes-Voigt equation ut − ν∆u − α 2 ∆ut + (u · ∇)u + ∇p = g(x) + εh dω dt in an arbitrary (bounded or unbounded  ...  Ball's energy equation method, we obtain a unique random attractor Aε for the random dynamical system generated by the equation.  ...  In non-autonomous case, the uniform attractor and pullback attractor were recently obtained in [30] and [1] respectively.  ... 
doi:10.1016/j.jmaa.2014.05.003 fatcat:zszkrg6nsnbrnhmiyggwjrkx4e
Szczepanski
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Quoc Bao Tang. "Dynamics of stochastic three dimensional Navier–Stokes–Voigt equations on unbounded domains." Journal of Mathematical Analysis and Applications 419.1 (2014) 583-605

Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces

Cung The Anh, ,Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam, Dang Thi Phuong Thanh, Nguyen Duong Toan, ,Department of Mathematics, Hung Vuong University, Nong Trang, Viet Tri, Phu Tho, Vietnam, ,Department of Mathematics, Haiphong University, 171 Phan Dang Luu, Kien An, Haiphong, Vietnam
2019 Evolution Equations and Control Theory  

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We consider a three-dimensional Navier-Stokes-Voigt equations with memory in lacking instantaneous kinematic viscosity, in presence of Ekman type damping and singularly oscillating external forces depending  ...  Under suitable assumptions on the memory term and on the external forces, we prove the existence and the uniform (w.r.t. ε) boundedness as well as the convergence as ε tends to 0 of uniform attractors  ...  This system was also proposed by Cao, Lunasin and Titi in [7] as a regularization, for small values of α, of the 3D Navier-Stokes equations for the sake of direct numerical simulations.  ... 
doi:10.3934/eect.2020039 fatcat:y6f5qkq2gnaerhmkp7jtgedtaq
Citation

Cung The Anh, ,Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam, Dang Thi Phuong Thanh, Nguyen Duong Toan, ,Department of Mathematics, Hung Vuong University, Nong Trang, Viet Tri, Phu Tho, Vietnam, ,Department of Mathematics, Haiphong University, 171 Phan Dang Luu, Kien An, Haiphong, Vietnam. "Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces." Evolution Equations and Control Theory 10.1 (2019) 0-0

Attractors for model of polymer solutions motion

Andrey Zvyagin
2018 Discrete and Continuous Dynamical Systems. Series A  

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Existence of trajectory, global and pullback attractors for an incompressible non-Newtonian fluid (namely, for the mathematical model which describes a weak aqueous polymer solutions motion) in 2D and  ...  For this aim the approximating topological method is effectively combined with the theory of attractors of trajectory spaces.  ...  This paper was financially supported by the Ministry of Education and Science of the Russian Federation on the program to improve the competitiveness of Peoples' Friendship University of Russia (RUDN University  ... 
doi:10.3934/dcds.2018269 fatcat:heengc75xbat5f6cbzqdaw7bj4
Citation

Andrey Zvyagin. "Attractors for model of polymer solutions motion." Discrete and Continuous Dynamical Systems. Series A 38.12 (2018) 6305-6325

Elementary Micromechanics of Heterogeneous Media [chapter]

Konstantin Z. Markov
2000 Modeling and Simulation in Science, Engineering and Technology  

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Institute for Mathematical Sciences at the University of Cambridge.  ...  Zimmerman for a number of very useful critical remarks and suggestions when reading a draft of this survey.  ...  or cylinders, forming a regular periodic array.  ... 
doi:10.1007/978-1-4612-1332-1_1 fatcat:bcwr2nlfbbfknm3hctgfhhbfyy
Citation

Konstantin Z. Markov. "Elementary Micromechanics of Heterogeneous Media." Modeling and Simulation in Science, Engineering and Technology (2000) 1-162

APM 2017. Book of abstracts [article]

"Advanced Problems In Mechanics (APM 2017)", International Conference (45; 2017; St. Petersburg, Russia), Russian Academy Of Sciences. Institute For Problems In Mechanical Engineering, University, Peter The Great St. Petersburg Polytechnic
2017

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One convenient way to account for this is through the introduction of second spatial (Laplacian) and time (inertia) derivatives of the pertinent mechanical and chemistry variables in the constitutive equations  ...  Kernel transforms of the integral equations are constructed numerically.  ...  This research has been supported by the Russian Foundation for Basic Research (14-01-00742, 16-29-01092), by the President Grant for Support of Leading Science Schools of Russian Federation (NSh-5436.2014.1  ... 
doi:10.18720/spbpu/2/k17-23 fatcat:us6nhplc3rbhrgowwocdqa2wrq
lang:ru
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"Advanced Problems In Mechanics (APM 2017)", International Conference (45; 2017; St. Petersburg, Russia), Russian Academy Of Sciences. Institute For Problems In Mechanical Engineering, University, Peter The Great St. Petersburg Polytechnic. "APM 2017. Book of abstracts." (2017)