Pavel Plotnikov

Lavrentʹev Institute of Hydro (Fluid) Dynamics, Siberian Branch Russian Academy of Sciences, Novosibirsk

Concentrations in weak solutions of the compressible Navier-Stokes equations

We use Di Perna and Majda generalization of Young measure to describe the concentrations in sequences of rotationally symmetric solutions to the compressible Navier–Stokes equations with critical and supercritical adiabatic exponents. We prove that concentrations of the energy tensor are supported on the symmetry axis. We also prove that the energy concentration matrix has only one nonzero entry, which corresponds to a jet directed along the symmetry axis. Moreover, the mollification of the concentration measure with respect to time variable is an absolutely continuous measure on the symmetry axis. The density of this measure belongs to some Sobolev space.