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GLOBAL UNIQUE SOLUTIONS FOR THE INHOMOGENEOUS NAVIER-STOKES EQUATION WITH ONLY BOUNDED DENSITY, IN CRITICAL REGULARITY SPACES
We here aim at proving the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density is discontinuous and the initial velocity has critical regularity. Assuming that the initial density is close to a positive constant, we obtain global existence and …