American Institute of Mathematical Sciences

Advanced
November  2009, 8(6): 1991-2012. doi: 10.3934/cpaa.2009.8.1991

Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations

Yuming Qin 1, , Lan Huang 2, and  Zhiyong Ma 2,

1. 

Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2. 

College of Information Science and Technology, Donghua University, Shanghai 201620

Received  November 2008 Revised  April 2009 Published  August 2009

This paper is concerned with the global existence and exponential stability of weak solutions in $H^4$ for a real viscous heat-conducting flow with shear viscosity in a bounded domain $\Omega=(0,1)$ . Some new ideas and more delicate estimates are introduced to prove these results.
Keywords: shear viscosity., a uniform priori estimates, Global existence, exponential stability.
Mathematics Subject Classification: Primary: 35B30, 35B40; Secondary: 35Q3.
Citation: Yuming Qin, Lan Huang, Zhiyong Ma. Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1991-2012. doi: 10.3934/cpaa.2009.8.1991
[1]

Jianguo Huang, Jun Zou. Uniform a priori estimates for elliptic and static Maxwell interface problems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 145-170. doi: 10.3934/dcdsb.2007.7.145
[2]

Théophile Chaumont-Frelet, Serge Nicaise, Jérôme Tomezyk. Uniform a priori estimates for elliptic problems with impedance boundary conditions. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2445-2471. doi: 10.3934/cpaa.2020107
[3]

Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure & Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002
[4]

Pavol Quittner, Philippe Souplet. A priori estimates of global solutions of superlinear parabolic problems without variational structure. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1277-1292. doi: 10.3934/dcds.2003.9.1277
[5]

Ovidiu Carja, Victor Postolache. A Priori estimates for solutions of differential inclusions. Conference Publications, 2011, 2011 (Special) : 258-264. doi: 10.3934/proc.2011.2011.258
[6]

Barbara Kaltenbacher, Irena Lasiecka. Global existence and exponential decay rates for the Westervelt equation. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 503-523. doi: 10.3934/dcdss.2009.2.503
[7]

Xueke Pu, Boling Guo. Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction. Kinetic & Related Models, 2016, 9 (1) : 165-191. doi: 10.3934/krm.2016.9.165
[8]

Victor Wasiolek. Uniform global existence and convergence of Euler-Maxwell systems with small parameters. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2007-2021. doi: 10.3934/cpaa.2016025
[9]

Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601
[10]

Younghun Hong, Changhun Yang. Uniform Strichartz estimates on the lattice. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3239-3264. doi: 10.3934/dcds.2019134
[11]

J. Huang, Marius Paicu. Decay estimates of global solution to 2D incompressible Navier-Stokes equations with variable viscosity. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4647-4669. doi: 10.3934/dcds.2014.34.4647
[12]

Gilbert Peralta. Uniform exponential stability of a fluid-plate interaction model due to thermal effects. Evolution Equations & Control Theory, 2020, 9 (1) : 39-60. doi: 10.3934/eect.2020016
[13]

Huafei Di, Yadong Shang, Jiali Yu. Existence and uniform decay estimates for the fourth order wave equation with nonlinear boundary damping and interior source. Electronic Research Archive, 2020, 28 (1) : 221-261. doi: 10.3934/era.2020015
[14]

Zhengce Zhang, Yan Li. Global existence and gradient blowup of solutions for a semilinear parabolic equation with exponential source. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 3019-3029. doi: 10.3934/dcdsb.2014.19.3019
[15]

Je-Chiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 601-623. doi: 10.3934/dcds.2008.21.601
[16]

Tae Gab Ha. Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6899-6919. doi: 10.3934/dcds.2016100
[17]

Nguyen Thanh Long, Hoang Hai Ha, Le Thi Phuong Ngoc, Nguyen Anh Triet. Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2020, 19 (1) : 455-492. doi: 10.3934/cpaa.2020023
[18]

Diogo A. Gomes, Gabriel E. Pires, Héctor Sánchez-Morgado. A-priori estimates for stationary mean-field games. Networks & Heterogeneous Media, 2012, 7 (2) : 303-314. doi: 10.3934/nhm.2012.7.303
[19]

D. Bartolucci, L. Orsina. Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates. Communications on Pure & Applied Analysis, 2005, 4 (3) : 499-522. doi: 10.3934/cpaa.2005.4.499
[20]

Gabrielle Nornberg, Delia Schiera, Boyan Sirakov. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3857-3881. doi: 10.3934/dcds.2020128

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (52)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences