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

Caochuan Ma

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: 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).

Keywords: Porous media equation; Global well-posedness; Decay estimate (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007482

DOI: 10.1016/j.amc.2022.127680

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