Global Existence of Strong and Weak Solutions to 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum

Abstract

We study the barotropic compressible Navier-Stokes system where the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. The system is subject to the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density allowed to vanish, we establish the global existence of strong and weak solutions without any restrictions on the size of initial value. To get over the difficulties brought by boundary, on the one hand, we apply Riemann mapping theorem and the pull back Green's function method to get a pointwise representation of the effective viscous flux. On the other hand, observing that the orthogonality is preserved under conformal mapping due to its preservation on the angle, we use the slip boundary conditions to reduce the integral representation to the desired commutator form whose singularities can be cancelled out by using the estimates on the spatial gradient of the velocity.

References in corpus (4)

• Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
• Existence and Exponential Growth of Global Classical Solutions to the Compressible Navier-Stokes Equations with Slip Boundary Conditions in 3D Bounded Domains

Cited by in corpus (1)

• Global Strong and Weak Solutions to the Initial-boundary-value Problem of 2D Compressible MHD System with Large Initial Data and Vacuum