Growth in the Muskat problem. (English) Zbl 1473.35442
Summary: We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criteria in terms of some norms of the initial data in critical spaces (\(\dot{W}^{1,\infty}\) and \(\dot{H}^{3/2}\)).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q86 | PDEs in connection with geophysics |
| 76S05 | Flows in porous media; filtration; seepage |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35D30 | Weak solutions to PDEs |
| 35D35 | Strong solutions to PDEs |
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