Remarks on Lifespan and Continuation Criteria of Two Dimensional Incompressible Fluid Models
Abstract
In this paper, we study the lifespan and continuation criteria of several two-dimensional incompressible fluid models. Motivated by a novel energy-vorticity formulation, combining linear transport estimate and a bootstrap argument, we are able to show several longtime existence results of two dimensional fluid models in the close-to-Euler regime. A byproduct of our approach is a new conditional BKM type result for the inhomogeneous incompressible Euler equation.
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