Break-down criterion for the water-wave equation

发布时间：2018-08-04 08:19

【摘要】：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+∫~T_0||(%絍, %紹)(t)||~6_(L∞)dt+∞,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.
[Abstract]: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 魏 of the free surface 危t, 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鈭圼0,T]||魏(t)||~(Lp鈭㎜~2 鈭珇T_0||(%绲，

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