The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)

The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided...

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Main Authors: Lai, S., Li, N., Wu, Yong Hong
Format: Journal Article
Published: SpringerOpen 2013
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/11326
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author Lai, S.
Li, N.
Wu, Yong Hong
author_facet Lai, S.
Li, N.
Wu, Yong Hong
author_sort Lai, S.
building Curtin Institutional Repository
collection Online Access
description The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided super bound estimate and a space-time higher-norm estimate for the equation are established to prove the existence of the global weak solution.
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institution Curtin University Malaysia
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spelling curtin-20.500.11937-113262017-09-13T14:53:18Z The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) Lai, S. Li, N. Wu, Yong Hong global weak solution Camassa-Holm type equation existence The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided super bound estimate and a space-time higher-norm estimate for the equation are established to prove the existence of the global weak solution. 2013 Journal Article http://hdl.handle.net/20.500.11937/11326 10.1186/1687-2770-2013-26 SpringerOpen fulltext
spellingShingle global weak solution
Camassa-Holm type equation
existence
Lai, S.
Li, N.
Wu, Yong Hong
The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title_full The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title_fullStr The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title_full_unstemmed The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title_short The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
title_sort existence of global weak solutions for a weakly dissipative camassa-holm equation in h1(r)
topic global weak solution
Camassa-Holm type equation
existence
url http://hdl.handle.net/20.500.11937/11326