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2001 A few remarks on the Camassa-Holm equation
Raphaël Danchin
Differential Integral Equations 14(8): 953-988 (2001).

Abstract

In the present paper, we use some standard a priori estimates for linear transport equations to prove the existence and uniqueness of solutions for the Camassa-Holm equation with minimal regularity assumptions on the initial data. We also derive some explosion criteria and a sharp estimate from below for the existence time. We finally address the question of global existence for certain initial data. This yields, among other things, a different proof for the existence and uniqueness of Constantin and Molinet's global weak solutions (see [9]).

Citation

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Raphaël Danchin. "A few remarks on the Camassa-Holm equation." Differential Integral Equations 14 (8) 953 - 988, 2001.

Information

Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35329
MathSciNet: MR1827098

Subjects:
Primary: 35Q53
Secondary: 35B30 , 35B40 , 35G25 , 76B03 , 76B15

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.14 • No. 8 • 2001
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