Global classical solution to the strip problem of 2D compressible Navier-Stokes system with vacuum and large initial data (Q6653875)

The article in question addresses the Navier-Stokes equations describing the motion of the two-dimensional barotropic compressible fluid. It is assumed, that the bulk viscosity \(\lambda\) is density dependent, in particular, \(\lambda = \lambda(\varrho) = b\varrho^\beta\) for some \(b,\beta>0\). All other parameters are standard: the shear viscosity is assumed to be positive constant, and the pressure \(P\) is given as \(P = P(\varrho) = R\varrho^\gamma\) for some \(R>0\) and \(\gamma>1\). This system is considered on a 2 dimensional infinite slab \(\Omega = \mathbb R\times \mathbb T\) where \(\mathbb T\) is a torus.\N\NThe main result of this paper concerns the existence of a unique global solution to the above system. The author provides conditions under which there is a strong solution and then he also provides additional requirements for the existence of a classical solution. It is of interest that obtained solutions exist globally in time even though there is no smallness assumption on the initial data.