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

  • Jerry L. bona (a1), Jonathan Cohen (a2) and Gang Wang (a3)
Abstract

In this paper, coupled systems

of Korteweg-de Vries type are considered, where u = u(x, t), v = v(x, t) are real-valued functions and where x, t∈R. Here, subscripts connote partial differentiation and

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,

for x ∈ ℝ. Under suitable conditions on P and Q, global well-posedness of this problem is established for initial data in the L 2-based Sobolev spaces Hs (ℝ) × Hs (ℝ) for any s > ‒3/4.

Copyright
COPYRIGHT: © Editorial Board of Nagoya Mathematical Journal 2014
References
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Nagoya Mathematical Journal
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