On the motion of viscous, compressible and heat-conducting liquids

Abstract

We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data - the weak strong uniqueness property.

References in corpus (3)

• Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
• Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
• A regularity criterion for the weak solutions to the Navier-Stokes-Fourier system

Cited by in corpus (1)

• Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis