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Zbl 0980.35150
Rodríguez-Blanco, Guillermo
On the Cauchy problem for the Camassa-Holm equation. (English)
[J] Nonlinear Anal., Theory Methods Appl. 46, No.3, A, 309-327 (2001). ISSN 0362-546X

From the introduction: We study local and global well-posedness with respect to the real-valued solutions of the Cauchy problem associated to the Camassa-Holm equation $$u_t- u_{xxt}+ 3uu_x= 2u_x u_{xx}+ u_{xxx},\quad x\in \bbfR,\ t\in \bbfR,$$ that was derived recently as a new model for dispersive shallow water waves.

MSC 2000:: *35Q53 KdV-like equations
76B15 Wave motions (fluid mechanics)

Keywords: Kato's theory; Camassa-Holm equation; local and global well-posedness; real-valued solutions; Cauchy problem; dispersive shallow water waves

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Zentralblatt MATH Berlin [Germany]