Global well-posedness for dissipative IPM with data close to a class of special solutions

Liangchen Zou

Global well-posedness for dissipative IPM with data close to a class of special solutions

Analysis of PDEs 2025-01-24 v1

Authors: Liangchen Zou

Abstract

In this paper, we consider the 2-D dissipative incompressible porous media (IPM) equation in both supercritical and subcritical cases. The dissipative IPM equation admits a class of special solutions of the form $\rho(x_1,x_2,t)=f(x_2,t)$ , which decay in the mode of the 1-D fractional heat equation. Our main result is the global well-posedness for the dissipative IPM equation with initial data close to this class of special solutions provided that $f$ satisfies certain regularity assumptions.

Keywords

dissipative IPM equation global well-posedness special solutions fractional heat equation supercritical/subcritical

Cite

@article{arxiv.2501.13248,
  title  = {Global well-posedness for dissipative IPM with data close to a class of special solutions},
  author = {Liangchen Zou},
  journal= {arXiv preprint arXiv:2501.13248},
  year   = {2025}
}

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