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- Title
Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L <sup>2</sup> Initial Data.
- Authors
Shang Bin Cui; Dong Gao Deng; Shuang Ping Tao
- Abstract
In this paper we study solvability of the Cauchy problem of the Kawahara equation $$ \partial _{t} u + au\partial _{x} u + \beta \partial ^{3}_{x} u + \gamma \partial ^{5}_{x} u = 0 $$ with L 2 initial data. By working on the Bourgain space X r,s ( R 2) associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H r ( R) and −1 < r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L 2( R).
- Subjects
NUMERICAL solutions to the Cauchy problem; NUMERICAL analysis; LINEAR differential equations; SOBOLEV spaces; INTERPOLATION
- Publication
Acta Mathematica Sinica, 2006, Vol 22, Issue 5, p1457
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-005-0710-6