Local Well-Posedness of the Inviscid Shallow Water Equations with Surface Tension
Xin Liu, Bingheng Yang
Abstract
We show that the inviscid shallow water equations with gravity and surface tension are locally well-posed in dimensions one and two. In contrast to previous works by Benzoni-Gavage, Danchin, and Descombes, we work only in the real-valued phase space and make use of the symmetry of the system. Our alternative proof for local well-posedness sheds some light on the symmetric structure of the shallow water system and can be used for further study, including designing numerical scheme, dispersion estimate, etc.
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