Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition
Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition
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DOI：
10.1155/s1073792804140555
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发表时间：
2004
影响因子：
1
通讯作者：
H. Takaoka;Y. Tsutsumi
中科院分区：
文献类型：
--
作者：
H. Takaoka;Y. Tsutsumi
研究了一维环面上修正的KdV方程柯西问题的时间局部适定性。我们证明了当1/2>；S>；3/8时，它在H·S中是局部适定的，但与S≥的1/2情形相比，解对初值的一致连续依赖性被打破了。这改进了Bourain(1993)的结果。
We study the time local well-posedness of the Cauchy problem for the modified KdV equation on the one-dimensional torus. We prove that when 1/2 > s > 3/8, it is locally well posed in H s , but the uniformly continuous dependence of solution on initial data breaks down in contrast to the case s ≥ 1/2. This improves the result of Bourgain (1993).