A local well-posed result for the fifth order KP-II initial value problem

作者：Li, Junfeng^*; Shi, Shaoguang

来源：Journal of Mathematical Analysis and Applications, 2013, 402(2): 679-692.

DOI：10.1016/j.jmaa.2013.01.069

• Kadomtsev-Petviashvili-II equation
• Well-posedness
• Strichartz estimates
• Bilinear estimates

The well-posedness of the real valued fifth order KP-II equation in Sobolev spaces H-s1,H-s2(R-2) has been studied by several authors. It was known to be locally well-posed in H-s,H-0(R-2) for s > -5/4 (see Hadac (2008) [3], Isaza et al. (2006) [5]). We are more interested in the case s = -5/4. We obtain the local well-posedness for s(1) >= -5/4, s(2) >= 0, which improves previous results by Saut and Tzvetkov (2000) [15] and by Isaza, Lopez and Mejia (2006) [5]. Moreover our main contribution is that we set up the global in time Strichartz estimates for the fifth order KP equation (no matter KP-I or KP-II equation) on dyadic pieces. And especially, on the low frequency part, we obtain a B-s -> L-4 estimate, in which we obtain 3/8 regularity which comes from the effect of partial derivative(-1)(x)partial derivative(2)(y) term.

• 出版日期2013-6-15
• 单位北京师范大学