Global existence, uniqueness, and stability hold for the 2D incompressible Navier-Stokes density patch problem at critical Besov regularity, with the Lipschitz boundary preserved and long-time dynamics reducing to rigid motion.
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On Lions' density patch problem at a critical level of regularity
Global existence, uniqueness, and stability hold for the 2D incompressible Navier-Stokes density patch problem at critical Besov regularity, with the Lipschitz boundary preserved and long-time dynamics reducing to rigid motion.