On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
The authors study the 2d Navier-Stokes system for a barotropic compressible fluid with constant dynamical viscosity and variable volume viscosity depending on the density of the fluid. For studying the ``time-global'' problem, the authors obtain a priori estimates with constants depending only on the data of the problem and the duration of the time interval and independent of the interval of existence of a local solution. Then, using already demonstrated theorems concerning existence and uniqueness for classical solutions on a sufficiently small time interval, the authors extend the local solution to the whole time interval. The existence of weak solutions is established by passage to the limit over a sequence of smooth solutions corresponding to the smoothed initial data.
scientific article; zbMATH DE number 917153
scientific article