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September 2014 Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities
Jerry L. Bona, Jonathan Cohen, Gang Wang
Nagoya Math. J. 215(none): 67-149 (September 2014). DOI: 10.1215/00277630-2691901


In this paper, coupled systems ut+uxxx+P(u,v)x=0, vt+vxxx+Q(u,v)x=0 of Korteweg–de Vries type are considered, where u=u(x,t), v=v(x,t) are real-valued functions and where x,tR. Here, subscripts connote partial differentiation and P(u,v)=Au2+Buv+Cv2andQ(u,v)=Du2+Euv+Fv2 are quadratic polynomials in the variables u and v. Attention is given to the pure initial-value problem in which u(x,t) and v(x,t) are both specified at t=0, namely, u(x,0)=u0(x)andv(x,0)=v0(x), for xR. Under suitable conditions on P and Q, global well-posedness of this problem is established for initial data in the L2-based Sobolev spaces Hs(R)×Hs(R) for any s>3/4.


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Jerry L. Bona. Jonathan Cohen. Gang Wang. "Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities." Nagoya Math. J. 215 67 - 149, September 2014.


Published: September 2014
First available in Project Euclid: 9 June 2014

zbMATH: 1372.35271
MathSciNet: MR3263526
Digital Object Identifier: 10.1215/00277630-2691901

Primary: 35Q35, 35Q51, 35Q53
Secondary: 42B35, 42B37, 76B15, 76B25, 86A05, 86A10

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal


Vol.215 • September 2014
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