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Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities.

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journal contribution
posted on 02.02.2015 by J. Bona, J. Cohen, G. Wang
In this paper, coupled systems ut + uxxx + P(u, v)x = 0, vt + vxxx + Q(u, v)x = 0, of KdV-type are considered, where u = u(x, t), v = v(x, t) are real-valued functions and x, t ∈ R. Here, subscripts connote partial differentiation and P(u, v) = Au2 + Buv + Cv2 and Q(u, v) = Du2 + Euv + F v2 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, viz. u(x, 0) = u0(x) and v(x, 0) = v0(x) for x ∈ R. 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 .

Funding

Research leave grants from the University Research Council of DePaul University and summer research grants from the College of Liberal Arts and Sciences of DePaul University.

History

Publisher

Duke University Press

issn

08934983

Issue date

01/01/2014

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