Global well-posedness of the 1D compressible Navier-Stokes equations with constant heat conductivity and nonnegative density

2018/01/29 by Jinkai Li, Li, Jinkai · 2 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1801.09395

Abstract

In this paper we consider the initial-boundary value problem to the one-dimensional compressible Navier-Stokes equations for idea gases. Both the viscous and heat conductive coefficients are assumed to be positive constants, and the initial density is allowed to have vacuum. Global existence and uniqueness of strong solutions is established for any H² initial data, which generalizes the well-known result of Kazhikhov--Shelukhin (Kazhikhov, A. V.; Shelukhin, V. V.: \emphUnique global solution with respect to time of initial boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273--282.) to the case that with nonnegative initial density.

Cited by

• Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum
• Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D

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