Global well-posedness and optimal decay estimate for the incompressible porous medium equation near a nontrivial equilibrium. (English) Zbl 1511.35282
Summary: 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 \(x_2\). The obtained decay rate is optimal in sense that this rate coincides with that of the linear system. In particular, the obtained \(L^\infty\) estimate of \(u_2\) improves the associated work in [T. M. Elgindi, Arch. Ration. Mech. Anal. 225, No. 2, 573–599 (2017; Zbl 1368.35218)].
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B35 | Stability in context of PDEs |
| 76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
| 76B70 | Stratification effects in inviscid fluids |
Citations:
Zbl 1368.35218References:
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