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This article is cited in 10 scientific papers (total in 10 papers)
On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg–de Vries Equation
S. I. Pokhozhaev Steklov Mathematical Institute of the Russian Academy of Sciences
Abstract:
We establish conditions on the initial data under which the Cauchy problem for the Korteweg–de Vries equation does not admit a solution global in $t>0$. The proof of the results is based on the nonlinear capacity method (Dokl. RAN, 357:5 (1997), 592–594). In closing, we provide an example.
Keywords:
blow-up, KdV equation, initial-boundary value problem, Cauchy problem, nonlinear capacity.
Received: 07.09.2011
Citation:
S. I. Pokhozhaev, “On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg–de Vries Equation”, Funktsional. Anal. i Prilozhen., 46:4 (2012), 51–60; Funct. Anal. Appl., 46:4 (2012), 279–286
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https://www.mathnet.ru/eng/faa3087https://doi.org/10.4213/faa3087 https://www.mathnet.ru/eng/faa/v46/i4/p51
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Abstract page: | 754 | Full-text PDF : | 271 | References: | 94 | First page: | 73 |
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