Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity
arXiv:2109.02822 · doi:10.1016/j.jde.2022.06.001
Abstract
In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler equations describing the motion of a liquid in an unbounded initial domain with moving boundary. The liquid is under the influence of gravity but without surface tension, and it is not assumed to be irrotational. We apply the tangential smoothing method introduced in [10,11] to construct the approximation system with energy estimates uniform in the smooth parameter. It should be emphasized that, when doing the nonlinear a priori estimates, we need neither the higher order wave equation of the pressure and delicate elliptic estimates, nor the higher regularity on the flow-map or initial vorticity. Instead, we adapt the Alinhac's good unknowns to the estimates of full spatial derivatives.
arXiv comment48 pages. Final version, accepted by J. Differ. Eq
References in corpus (13)
- Global well-posedness of the 3-D full water wave problem
- Well posedness for the motion of a compressible liquid with free surface boundary
- A priori estimates for the free-boundary 3-D compressible Euler equations in physical vacuum
- Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation
- Well-posedness of the plasma-vacuum interface problem
- Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics
- Two dimensional gravity water waves with constant vorticity: I. Cubic lifespan
- Local Well-posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics
- Local well-posedness for the motion of a compressible, self-gravitating liquid with free surface boundary
- A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
- On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid
- A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid
- On the lifespan of three-dimensional gravity water waves with vorticity