Global well-posedness for dissipative IPM with data close to a class of special solutions
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 (x1,x2,t)=f(x2,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.
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