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Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities. (English) Zbl 1372.35271

This paper deals with the local and global well-posedness for an initial value problem involving a coupled system of Korteweg-de Vries type equations with quadratic nonlinearities. Persistence of regularity is established. Explicit results for correction terms, that yield a functional whose time derivative is controlled in a certain manner, along with pointwise estimates for the relevant functional are obtained to conclude the main result relating to the global well-posedness for the initial value problem.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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