Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws

Liu, Tai-Ping; Zeng, Yanni

doi:10.1090/memo/0599

Cited by 153 publications

(170 citation statements)

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“…Therefore, our results greatly improve the previous ones due to [5,8,12,14,17,22,23] where some additional smallness conditions on the initial data are needed. [9,10] where he proved that the temperature is uniformly (in time) bounded from below and above locally in x and that global solutions are convergent locally in space as time goes to infinity.…”

Section: Remark 11 In Theorem 11 We Only Assume That the Initial Dsupporting

confidence: 65%

Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data

Liang

2015

Arch Rational Mech Anal

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This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous heatconducting perfect polytropic gas in unbounded domains. The temperature is proved to be bounded from below and above independently of both time and space. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity. Note that the initial data can be arbitrarily large. This result is proved by using elementary energy methods.

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Section: Remark 11 In Theorem 11 We Only Assume That the Initial Dsupporting

confidence: 65%

Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data

Liang

2015

Arch Rational Mech Anal

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“…In particular, the one-dimensional problem has been studied in many papers, for examples, [3,4,7,15,17,22,25] and so on. However, many fundamental problems for MHD are still open.…”

Section: Introductionmentioning

confidence: 99%

Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

Wang²

2010

Arch Rational Mech Anal

307

219

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Abstract. The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ > 3 2 and constant viscosity coefficients.

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“…The same Evans assumption has already been shown to imply long time stability of viscous profiles in the 1D case in [KK] for zero mass perturbations and [Z2,MaZ1,MaZ2,MaZ3,MaZ4,MaZ5,Z3,HZ,Ra] for general perturbations, and in the multidimensional case in [Z1, Z3, Z4] (for general perturbations); see also the important groundwork of [GZ, ZH, ZS] and [K1,K2,KS,LZe,H1,H2]. A treatment of the scalar multidimensional case (for which the Evans assumption always holds, by the maximum principle) may be found in [HoZ2,HoZ3].…”

Section: Part 1 Introductionmentioning

confidence: 73%

Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability

Guès¹,

Métivier

Williams

et al. 2004

J. Amer. Math. Soc.

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We use energy estimates to study the long time stability of multidimensional planar viscous shocks ψ ( x 1 ) \psi (x_1) for systems of conservation laws. Stability is proved for both zero mass and nonzero mass perturbations, and some of the results include rates of decay in time. Shocks of any strength are allowed, subject to an appropriate Evans function condition. The main tools are a conjugation argument that allows us to replace the eigenvalue equation by a problem in which the x 1 x_1 dependence of the coefficients is removed and degenerate Kreiss-type symmetrizers designed to cope with the vanishing of the Evans function for zero frequency.

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Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws

Cited by 153 publications

References 0 publications

Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data

Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data

Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability

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