On global existence and large-time behaviour of weak solutions to the compressible barotropic Navier--Stokes Equations on ${\mathbb{T}}^2$ with density-dependent bulk viscosity: beyond the Va\uıgant--Kazhikhov regime

Siran Li, Jianing Yang

We are concerned with the compressible barotropic Navier--Stokes equations for a $\gamma$-law gas with density-dependent bulk viscosity coefficient $\lambda =\lambda (\rho )={\rho }^{\beta }$ on the two-dimensional p…