Optimal Lp - Lq convergence rates for the compressible Navier-Stokes equations with potential force

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

149 Scopus Citations
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)220-233
Journal / PublicationJournal of Differential Equations
Volume238
Issue number1
Publication statusPublished - 1 Jul 2007

Abstract

In this paper, we are concerned with the optimal Lp - Lq convergence rates for the compressible Navier-Stokes equations with a potential external force in the whole space. Under the smallness assumption on both the initial perturbation and the external force in some Sobolev spaces, the optimal convergence rates of the solution in Lq-norm with 2 ≤ q ≤ 6 and its first order derivative in L2-norm are obtained when the initial perturbation is bounded in Lp with 1 ≤ p <6 / 5. The proof is based on the energy estimates on the solution to the nonlinear problem and some Lp - Lq estimates on the semigroup generated by the corresponding linearized operator. © 2007 Elsevier Inc. All rights reserved.

Research Area(s)

  • Compressible Navier-Stokes equations, Lp - Lq estimate, Optimal convergence rate, Potential force

Citation Format(s)