Unique solvability of compressible micropolar viscous fluids

Heat Convection of Compressible Viscous Fluids. I

The stationary problem for the heat convection of compressible fluid is considered around the equilibrium solution with the external forces in the horizontal strip domain z0 < z < z0 + 1 and it is proved that the solution exists uniformly with respect to z0 ≥ Z0 . The limit system as z0 → +∞ is the Oberbeck-Boussinesq equations. Mathematics Subject Classification (2010). Primary 35Q35; Secondar...

Mathematical theory of compressible, viscous, and heat conducting fluids

We review some recent results on the Navier–Stokes–Fourier system governing the evolution of a general compressible, viscous, and heat conducting fluid. We discuss several concepts of weak solutions, in particular, using the implications of the Second law of thermodynamics. We introduce the concept of relative entropy and dissipative solution and show the principle of weak-strong uniqueness. We...

Problems in the Theory of Viscous Compressible Fluids

One-dimensional flow of a compressible viscous micropolar fluid: The Cauchy problem

The Cauchy problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. A corresponding initial-boundary value problem has a unique strong solution on ]0, 1[×]0, T [, for each T > 0. By using this result we construct a sequence of approximate solutions which converges to a sol...

Nonhomogeneous Boundary Value Problem for One-Dimensional Compressible Viscous Micropolar Fluid Model: Regularity of the Solution

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Hölder continuous on 0, 1 and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on 0, 1 × 0, T , for each T > 0. The proof is b...