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| 摘要: |
| 本文研究了KdVKS方程ut+δ∂x3u+μ（∂x4u+∂x2u）+α（∂xu）2=0的Cauchy问题.利用Tao的[k；Z]乘子范数估计的方法，在Sobolev空间Hs（R），s >-1中证明了初值问题的局部适定性，结论改进了现有的Biagioni等的结果. |
| 关键词: KdVKS方程 局部适定性 Cauchy问题 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:Supported by National Natural Science Foundation of China (10771166); Foundation of Henan Educational Committee (14B110028; 16A110007). |
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| ON THE LOCAL WELL-POSEDNESS FOR THE KDVKS EQUATION |
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WANG Hong-wei,ZHANG Yuan-yuan
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| Abstract: |
| In this paper, we consider the Cauchy problem for the KdVKS equation ut + δ∂x3u + μ(∂x4u +∂x2u) + α(∂xu)2=0. By means of the[k; Z] multiplier norm method of Tao, we prove the associated initial value problem is locally well-posed in Sobolev spaces Hs(R) for s > -1, which improves the conclusions drawn by Biagioni et al. |
| Key words: KdVKS equation local well-posedness Cauchy problem |
