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arXiv · 2211.06952

Maximal $L^1$-regularity and free boundary problems for the incompressible Navier-Stokes equations in critical spaces

Takayoshi Ogawa·Senjo Shimizu
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Abstract

Time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space and special structures of the quasi-linear term appearing from the Lagrangian transform of the coordinate.

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Takayoshi Ogawa, Senjo Shimizu. 2022-11-13. Maximal $L^1$-regularity and free boundary problems for the incompressible Navier-Stokes equations in critical spaces. https://arxiv.org/abs/2211.06952

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