Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 215 (2014), 67-149.
Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities
In this paper, coupled systems of Korteweg–de Vries type are considered, where , are real-valued functions and where . Here, subscripts connote partial differentiation and are quadratic polynomials in the variables and . Attention is given to the pure initial-value problem in which and are both specified at , namely, for . Under suitable conditions on and , global well-posedness of this problem is established for initial data in the -based Sobolev spaces for any .
Nagoya Math. J., Volume 215 (2014), 67-149.
First available in Project Euclid: 9 June 2014
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q35: PDEs in connection with fluid mechanics 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 42B35: Function spaces arising in harmonic analysis 42B37: Harmonic analysis and PDE [See also 35-XX] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B25: Solitary waves [See also 35C11] 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]
Bona, Jerry L.; Cohen, Jonathan; Wang, Gang. Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities. Nagoya Math. J. 215 (2014), 67--149. doi:10.1215/00277630-2691901. https://projecteuclid.org/euclid.nmj/1402319947