Almost Global Existence of Solutions to the Kadomtsev-Petviashvili Equations

作者：Hayashi Nakao^*; Naumkin Pavel I; Niizato Tomoyuki

来源：Funkcialaj Ekvacioj-Serio Internacia, 2012, 55(1): 157-168.

DOI：10.1619/fesi.55.157

• Kadomtsev-Petviashvili equations
• Almost global existence

We consider the Cauchy problem for the Kadomtsev-Petviashvili equations u(t) + u(xxx) + sigma partial derivative(-1)(x)u(yy) = -(u(2))(x), (x, y) is an element of R-2, t is an element of R, u(0, x, y) = u(0)(x, y), (x, y) is an element of R-2, where sigma = 1 or sigma = -1, partial derivative(-1)(x) = integral(x)(-infinity) dx%26apos;. We prove that the maximal existence time T is estimated from below as T %26gt;= exp(C/epsilon), where epsilon denotes the size of the initial data, C %26gt; 0 is a constant.

• 出版日期2012-4