Local and Global Existence of Solutions to
Initial Value Problems of Modified Nonlinear
Kawahara Equations |
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Authors: | Shuang Ping Tao Shang Bin Cui |
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Institution: | (1) Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China;(2) Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China |
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Abstract: | This paper is devoted to studying the initial value problem of the modified nonlinear
Kawahara equation
(x,t) ∈ R
2. We first establish several Strichartz
type estimates for the fundamental solution of the corresponding linear problem. Then we apply such
estimates to prove local and global existence of solutions for the initial value problem of the modified
nonlinear Karahara equation. The results show that a local solution exists if the initial function
u
0(x) ∈ H
s
(R) with s ≥ 1/4, and a global solution exists if s ≥ 2.
Supported by NWNU-KJCXGC-212 and NWNU-QNJSJJ |
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Keywords: | Kawahara equation Initial value problem Solution Local existence Global existence |
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