We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the ...We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the free surface, and the outer normal derivative ？P/？n of the pressure P satisfy sup t∈[0,T]｜｜κ（t）｜｜Lp∩L^2＋∫0^T｜｜（▽V, ▽B）（t）｜｜L∞^6dt〈＋∞,inf （t,x,y）∈[0,T]×Σ_t- P/ n（t, x, y）≥c0,for some p 〉 2d and c_0〉 0, then the solution can be extended after t = T.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11371039 and 11425103)
文摘We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the free surface, and the outer normal derivative ？P/？n of the pressure P satisfy sup t∈[0,T]｜｜κ（t）｜｜Lp∩L^2＋∫0^T｜｜（▽V, ▽B）（t）｜｜L∞^6dt〈＋∞,inf （t,x,y）∈[0,T]×Σ_t- P/ n（t, x, y）≥c0,for some p 〉 2d and c_0〉 0, then the solution can be extended after t = T.
