Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D
Jinkai Li
Abstract
Abstract In this paper, the initial-boundary value problem of the one-dimensional full compressible Navier–Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any H 1 initial data. The initial density is assumed only to be nonnegative, and, thus, is not necessary to be uniformly away from vacuum. Comparing with the well-known result of Kazhikhov and Shelukhin (1977 J. Appl. Math. Mech . 41 273–282), the heat conductive coefficient is zero in this paper, and the initial vacuum is allowed.
Topics & Concepts
MathematicsCompressibilityConstant (computer programming)Zero (linguistics)ViscosityElectrical conductorMathematical analysisInitial value problemCompressible flowHeat equationThermal conductivityConductivityElectrical resistivity and conductivityConstant coefficientsMechanicsThermodynamicsAbsolute zeroThermal conductionNavier-Stokes equation solutionsStability and Controllability of Differential EquationsComputational Fluid Dynamics and Aerodynamics