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- W4300881453 abstract "We prove a global existence result of a unique strong solution in $dot H^{5/2} cap dot H^{3/2}$ with small $dot H^{3/2}$ semi-norm for the 2D Muskat problem, hence allowing the interface to have arbitrary large finite slopes and finite energy (thanks to the $L^{2}$ maximum principle). The proof is based on the use of a new formulation of the Muskat equation that involves oscillatory terms. Then, a careful use of interpolation inequalities in homogeneneous Besov spaces allows us to close the {emph{a priori}} estimates." @default.
- W4300881453 created "2022-10-04" @default.
- W4300881453 creator A5070145769 @default.
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- W4300881453 date "2018-03-20" @default.
- W4300881453 modified "2023-09-27" @default.
- W4300881453 title "Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$" @default.
- W4300881453 doi "https://doi.org/10.48550/arxiv.1803.07528" @default.
- W4300881453 hasPublicationYear "2018" @default.
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