Abstract
In this paper, we prove the global well-posedness of free boundary problems of the Navier-Stokes equations in a bounded domain with surface tension. The velocity field is obtained in the Lp in time Lq in space maximal regularity class, (2<p<∞, N<q<∞, and 2/p+N/q<1), under the assumption that the initial domain is close to a ball and initial data are sufficiently small. The essential point of our approach is to drive the exponential decay theorem in the Lp-Lq framework for the linearized equations with the help of maximal Lp-Lq regularity theory for the Stokes equations with free boundary conditions and spectral analysis of the Stokes operator and the Laplace-Beltrami operator.
Original language | English |
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Pages (from-to) | 117-152 |
Number of pages | 36 |
Journal | Evolution Equations and Control Theory |
Volume | 7 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- Free boundary problems
- Global well-posedness
- Navier-stokes equations
- Surface tension
ASJC Scopus subject areas
- Modelling and Simulation
- Control and Optimization
- Applied Mathematics