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

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 $H^2$ initial data, which generalizes the well-known result of Kazhikhov--Shelukhin (Kazhikhov, A. V.; Shelukhin, V. V.: \emph{Unique 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.

References in corpus (5)

• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data
• On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
• Non-Existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier-Stokes Equations
• Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum

Cited by in corpus (3)

• Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity
• 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