带表面张力的无粘浅水方程的局部适定性
Local Well-Posedness of the Inviscid Shallow Water Equations with Surface Tension
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中文总结 AI 辅助
该研究证明带重力和表面张力的无粘浅水方程在一、二维空间局部适定，通过利用系统对称性在实值相空间给出替代证明，其成果可用于数值格式设计等后续研究。
中文摘要 AI 辅助
我们证明了带重力和表面张力的无粘浅水方程在一维和二维空间中是局部适定的。与Benzoni-Gavage、Danchin和Descombes之前的工作不同，我们仅在实值相空间中研究，并利用了该系统的对称性。我们对局部适定性的替代证明揭示了浅水系统的对称结构，可用于进一步研究，包括数值格式设计、色散估计等。
英文摘要
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.
