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Endpoint Compactness and Finite-Energy Weak Solutions for the 2D Isothermal Compressible Navier-Stokes
We prove global existence of finite-energy renormalized weak solutions to the 2D isothermal compressible Navier--Stokes equations in bounded $C^2$ domains with no-slip boundary conditions. The initial data are arbitrary in the natural energy class, allowing vacuum and unbounded density. This resolve
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