This paper is devoted to studying the initial-value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces X s,b (R 2 ) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I-method as well as L 2 c
On the local regularity of the KP-I equation in anisotropic Sobolev space
โ Scribed by Zihua Guo; Lizhong Peng; Baoxiang Wang
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 225 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0021-7824
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๐ SIMILAR VOLUMES
In this paper we establish the local and global well-posedness of the real valued fifth order Kadomtsev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves Saut-Tzvetkov's one and our global well-posedness gives an affi
We prove that C2\*" (a) solutions of problem (1.2) below are in H"+2(i2) for all m E IN, if f and the coefficients are in Hm(52) n Cola (a) . Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11) below. of IR\* ; in th
## Abstract In this paper, we consider local wellโposedness and illโposedness questions for the fractal Burgers equation. First, we obtain the wellโposedness result in the critical Sobolev space. We also present an unconditional uniqueness result. Second, we show the illโposedness from the point of
The generalized Burgers equation @tu -@xxu + @xu k+1 = 0, with initial data u0 in homogeneous Sobolev spaces are investigated. The starting point of this work is the construction of solutions in . If in addition, the initial data belongs to Lp;s then the obtained solution is actually in L โ ([0; โ)
## Abstract In this paper, we investigate the Stokes system and the biharmonic equation in a halfโspace of โ^__n__^. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity