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Global well-posedness and optimal decay estimate for the incompressible porous medium equation near a nontrivial equilibrium

Applied Mathematics and Computation, ISSN: 0096-3003, Vol: 440, Page: 127680
2023
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Article Description

In this paper, we prove global well-posedness and optimal decay estimate of solution to the 2D inviscid incompressible porous medium equation near a nontrivial equilibrium x2. The obtained decay rate is optimal in sense that this rate coincides with that of the linear system. In particular, the obtained L∞ estimate of u2 improves the associated work in (T.M. Elgindi, Arch. Ration. Mech. Anal. 2017).

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