• 科學研究
    報告題目:

    Local Well-Posedness for the Motion of a Compressible Water Wave with Vorticity

    報告人:

    Prof. Chenyun Luo (香港中文大學)

    報告時間:

    報告地點:

    騰訊會議 ID:507 884 682

    報告摘要:

    We establish the local well-posedness for the motion of a compressible gravity water wave in 3D with vorticity taken into account. It is well-known that the existence for the free-boundary problem is not a direct consequence of the apriori estimate, since the approximate problems destroy the symmetry enjoyed by the original problem. We adapt the tangential smoothing introduced by Coutand-Shkoller to construct the approximation system with energy estimates uniform in the smoothing parameter. It should be emphasized that, when doing the a priori estimates, we need neither the higher-order wave equation of the pressure and delicate elliptic estimates nor the higher regularity assumption on the initial vorticity. Instead, we adapt the Alinhac good unknown method to the estimates of full spatial derivatives.

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