In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in S...In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption that $\frac{{\partial p}}{{\partial n}}(\xi )\left| {_{t = 0} } \right. \leqslant - 2c_0 < 0$ being restricted to the initial surface.展开更多
A calculation method based on the Bloch theorem is developed for the gravity surface waves over the periodic bottoms of large undulations. The study shows the existence of comparable high-order bandgaps, which are dem...A calculation method based on the Bloch theorem is developed for the gravity surface waves over the periodic bottoms of large undulations. The study shows the existence of comparable high-order bandgaps, which are demonstrated to result from the higher-order Bragg resonances, i.e. the resonant interactions between surface waves and the harmonic components of the fluctuating bottom. It is also shown that the band widths of the high-order gaps are quite sensitive to the amplitudes of high-order harmonics of the bottom.展开更多
基金the National Natural Science Foundation of China(Grant Nos.10525101,10421101 and 10601002)the innovation grant from Chinese Academy of Sciences
文摘In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption that $\frac{{\partial p}}{{\partial n}}(\xi )\left| {_{t = 0} } \right. \leqslant - 2c_0 < 0$ being restricted to the initial surface.
基金Supported by the National Science Foundation of China under Grant Nos 19925414 and 10474045, and the Research Fund for the Doctoral Program of Higher Education of China under Grant No 20050284018.
文摘A calculation method based on the Bloch theorem is developed for the gravity surface waves over the periodic bottoms of large undulations. The study shows the existence of comparable high-order bandgaps, which are demonstrated to result from the higher-order Bragg resonances, i.e. the resonant interactions between surface waves and the harmonic components of the fluctuating bottom. It is also shown that the band widths of the high-order gaps are quite sensitive to the amplitudes of high-order harmonics of the bottom.
