Optimal convergence rates for the compressible Navier-Stokes equations with potential forces

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)737-758
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume17
Issue number5
Publication statusPublished - May 2007

Abstract

For the viscous and heat-conductive fluids governed by the compressible Navier-Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the L p - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded. © World Scientific Publishing Company.

Research Area(s)

  • Energy estimates, Navier-Stokes equations, Optimal convergence rate