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Mathematics > Analysis of PDEs

arXiv:1804.08490 (math)
[Submitted on 20 Apr 2018 (v1), last revised 28 Apr 2021 (this version, v3)]

Title:Global existence of quasi-stratified solutions for the confined IPM equation

Authors:Angel Castro, Diego Córdoba, Daniel Lear
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Abstract:In this paper, we consider a confined physical scenario to prove global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the stability of stratified solutions, combined with an additional structure of our initial perturbation, which allows us to get rid of the boundary terms in the energy estimates.
Comments: 24 pages. Updated funding
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.08490 [math.AP]
  (or arXiv:1804.08490v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.08490
Related DOI: https://doi.org/10.1007/s00205-018-1324-3

Submission history

From: Angel Castro [view email]
[v1] Fri, 20 Apr 2018 11:14:09 UTC (28 KB)
[v2] Mon, 1 Oct 2018 10:06:35 UTC (32 KB)
[v3] Wed, 28 Apr 2021 08:26:55 UTC (32 KB)
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