-
Previous Article
Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families
- DCDS Home
- This Issue
-
Next Article
Steady asymmetric vortex pairs for Euler equations
On convergence to equilibria of flows of compressible viscous fluids under in/out–flux boundary conditions
1. | Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan |
2. | Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic, Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany |
3. | IMATH, EA 2134, Université de Toulon, BP 20132, 83957 La Garde, France |
We consider the barotropic Navier–Stokes system describing the motion of a compressible Newtonian fluid in a bounded domain with in and out flux boundary conditions. We show that if the boundary velocity coincides with that of a rigid motion, all solutions converge to an equilibrium state for large times.
References:
[1] |
G. Avalos and P. G. Geredeli,
Exponential stability of a nondissipative, compressible flow-structure PDE model, J. Evol. Equ., 20 (2020), 1-38.
doi: 10.1007/s00028-019-00513-9. |
[2] |
T. Chang, B. J. Jin and A. Novotný,
Compressible Navier-Stokes system with general inflow-outflow boundary data, SIAM J. Math. Anal., 51 (2019), 1238-1278.
doi: 10.1137/17M115089X. |
[3] |
H. J. Choe, A. Novotný and M. Yang,
Compressible Navier-Stokes system with hard sphere pressure law and general inflow-outflow boundary conditions, J. Differential Equations, 266 (2019), 3066-3099.
doi: 10.1016/j.jde.2018.08.049. |
[4] |
E. Feireisl and H. Petzeltová,
On the zero-velocity-limit solutions to the Navier-Stokes equations of compressible flow, Manuscr. Math., 97 (1998), 109-116.
doi: 10.1007/s002290050089. |
[5] |
E. Feireisl and H. Petzeltová,
Large-time behaviour of solutions to the Navier-Stokes equations of compressible flow, Arch. Rational Mech. Anal., 150 (1999), 77-96.
doi: 10.1007/s002050050181. |
[6] |
E. Feireisl and D. Pražák, Asymptotic Behavior of Dynamical Systems in Fluid Mechanics, AIMS, Springfield, 2010. Google Scholar |
[7] |
P. G. Geredeli, A time domain approach for the exponential stability of a linearized compressible flow–structure pde system, Math. Meth. Appl. Sci., 2020. Early view. Google Scholar |
[8] |
V. Girinon,
Navier-Stokes equations with nonhomogeneous boundary conditions in a bounded three-dimensional domain, J. Math. Fluid Mech., 13 (2011), 309-339.
doi: 10.1007/s00021-009-0018-x. |
[9] |
Y.-S. Kwon and A. Novotný, Dissipative solutions to compressible Navier–Stokes equations with general inflow-outflow data: Existence, stability and weak strong uniqueness, J. Math. Fluid Mech., 2021 (in press). arXiv: 1905.02667. Google Scholar |
[10] |
B. Melinand and K. Zumbrun,
Existence and stability of steady compressible Navier-Stokes solutions on a finite interval with noncharacteristic boundary conditions, Phys. D, 394 (2019), 16-25.
doi: 10.1016/j.physd.2019.01.006. |
[11] |
A. Novotný and I. Straškraba,
Stabilization of weak solutions to compressible Navier-Stokes equations, J. Math. Kyoto Univ., 40 (2000), 217-245.
doi: 10.1215/kjm/1250517713. |
[12] |
A. Novotný and I. Straškraba,
Convergence to equilibria for compressible Navier-Stokes equations with large data, Annali Mat. Pura Appl., 179 (2001), 263-287.
doi: 10.1007/BF02505958. |
[13] |
Y. Shibata and K. Tanaka,
Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid, Comput. Math. Appl., 53 (2007), 605-623.
doi: 10.1016/j.camwa.2006.02.030. |
[14] |
S. Ukai, T. Yang and H. Zhao,
Convergence rate for the compressible Navier-Stokes equations with external force, J. Hyperbolic Differ. Equ., 3 (2006), 561-574.
doi: 10.1142/S0219891606000902. |
show all references
References:
[1] |
G. Avalos and P. G. Geredeli,
Exponential stability of a nondissipative, compressible flow-structure PDE model, J. Evol. Equ., 20 (2020), 1-38.
doi: 10.1007/s00028-019-00513-9. |
[2] |
T. Chang, B. J. Jin and A. Novotný,
Compressible Navier-Stokes system with general inflow-outflow boundary data, SIAM J. Math. Anal., 51 (2019), 1238-1278.
doi: 10.1137/17M115089X. |
[3] |
H. J. Choe, A. Novotný and M. Yang,
Compressible Navier-Stokes system with hard sphere pressure law and general inflow-outflow boundary conditions, J. Differential Equations, 266 (2019), 3066-3099.
doi: 10.1016/j.jde.2018.08.049. |
[4] |
E. Feireisl and H. Petzeltová,
On the zero-velocity-limit solutions to the Navier-Stokes equations of compressible flow, Manuscr. Math., 97 (1998), 109-116.
doi: 10.1007/s002290050089. |
[5] |
E. Feireisl and H. Petzeltová,
Large-time behaviour of solutions to the Navier-Stokes equations of compressible flow, Arch. Rational Mech. Anal., 150 (1999), 77-96.
doi: 10.1007/s002050050181. |
[6] |
E. Feireisl and D. Pražák, Asymptotic Behavior of Dynamical Systems in Fluid Mechanics, AIMS, Springfield, 2010. Google Scholar |
[7] |
P. G. Geredeli, A time domain approach for the exponential stability of a linearized compressible flow–structure pde system, Math. Meth. Appl. Sci., 2020. Early view. Google Scholar |
[8] |
V. Girinon,
Navier-Stokes equations with nonhomogeneous boundary conditions in a bounded three-dimensional domain, J. Math. Fluid Mech., 13 (2011), 309-339.
doi: 10.1007/s00021-009-0018-x. |
[9] |
Y.-S. Kwon and A. Novotný, Dissipative solutions to compressible Navier–Stokes equations with general inflow-outflow data: Existence, stability and weak strong uniqueness, J. Math. Fluid Mech., 2021 (in press). arXiv: 1905.02667. Google Scholar |
[10] |
B. Melinand and K. Zumbrun,
Existence and stability of steady compressible Navier-Stokes solutions on a finite interval with noncharacteristic boundary conditions, Phys. D, 394 (2019), 16-25.
doi: 10.1016/j.physd.2019.01.006. |
[11] |
A. Novotný and I. Straškraba,
Stabilization of weak solutions to compressible Navier-Stokes equations, J. Math. Kyoto Univ., 40 (2000), 217-245.
doi: 10.1215/kjm/1250517713. |
[12] |
A. Novotný and I. Straškraba,
Convergence to equilibria for compressible Navier-Stokes equations with large data, Annali Mat. Pura Appl., 179 (2001), 263-287.
doi: 10.1007/BF02505958. |
[13] |
Y. Shibata and K. Tanaka,
Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid, Comput. Math. Appl., 53 (2007), 605-623.
doi: 10.1016/j.camwa.2006.02.030. |
[14] |
S. Ukai, T. Yang and H. Zhao,
Convergence rate for the compressible Navier-Stokes equations with external force, J. Hyperbolic Differ. Equ., 3 (2006), 561-574.
doi: 10.1142/S0219891606000902. |
[1] |
Andrea Giorgini, Roger Temam, Xuan-Truong Vu. The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 337-366. doi: 10.3934/dcdsb.2020141 |
[2] |
Duy Phan. Approximate controllability for Navier–Stokes equations in $ \rm3D $ cylinders under Lions boundary conditions by an explicit saturating set. Evolution Equations & Control Theory, 2021, 10 (1) : 199-227. doi: 10.3934/eect.2020062 |
[3] |
Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020348 |
[4] |
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110 |
[5] |
Jean-Claude Saut, Yuexun Wang. Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1133-1155. doi: 10.3934/dcds.2020312 |
[6] |
Franck Davhys Reval Langa, Morgan Pierre. A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 653-676. doi: 10.3934/dcdss.2020353 |
[7] |
Linglong Du, Min Yang. Pointwise long time behavior for the mixed damped nonlinear wave equation in $ \mathbb{R}^n_+ $. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020033 |
[8] |
Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020398 |
[9] |
Fang Li, Bo You. On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021024 |
[10] |
Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415 |
[11] |
Xuhui Peng, Rangrang Zhang. Approximations of stochastic 3D tamed Navier-Stokes equations. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5337-5365. doi: 10.3934/cpaa.2020241 |
[12] |
Zhiting Ma. Navier-Stokes limit of globally hyperbolic moment equations. Kinetic & Related Models, 2021, 14 (1) : 175-197. doi: 10.3934/krm.2021001 |
[13] |
Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 |
[14] |
Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020336 |
[15] |
Rong Wang, Yihong Du. Long-time dynamics of a diffusive epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020360 |
[16] |
Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3909-3955. doi: 10.3934/dcds.2020036 |
[17] |
Leanne Dong. Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020352 |
[18] |
Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces. Evolution Equations & Control Theory, 2021, 10 (1) : 1-23. doi: 10.3934/eect.2020039 |
[19] |
Xin-Guang Yang, Rong-Nian Wang, Xingjie Yan, Alain Miranville. Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020408 |
[20] |
Xiaopeng Zhao, Yong Zhou. Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 795-813. doi: 10.3934/dcdsb.2020142 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]