Isothermal Navier-Stokes Equations and Radon Transform

In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a problem with no-slip condition for nonstationary motion of viscous compressible isothermal fluid. However, the technique of modeling and analysis presented here is general and can be used for 3D problems.

Steady 3D viscous compressible flows with adiabatic exponent $gammain (1,infty)$

The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak solution under the assumption that the adiabatic exponent satisfies $gamma>1$ is proved. These results cover the cases of monoatomic, diatomic, and polyatomic gases.