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A blow-up criterion for the inhomogeneous incompressible Euler equations. (English) Zbl 1437.35553

Summary: In this paper, we first show the existence of local-in-time solutions the inhomogeneous incompressible Euler equations in \(\mathbb{R}^3\). We then derive a refined blow-up criterion of these solutions.

MSC:

35Q31 Euler equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B44 Blow-up in context of PDEs
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