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On the Cauchy problem for a coupled system of KdV equations

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  • We study some questions related to the well-posedness for the initial value problem associated to the system

    $u_{t}+u_{x x x}+a_3 v_{x x x}+u u_{x}+a_1 v v_{x}+a_2(uv)_x =0,$

    $b_1 v_{t}+v_{x x x}+b_2 a_3 u_{x x x}+v v_{x}+b_2 a_2 u u_{x}+b_2 a_1(uv)_x=0.$

    Using recent methods, we prove a sharp local result in Sobolev spaces. We also prove global result under some conditions on the coefficients.

    Mathematics Subject Classification: 35Q35, 35Q53.


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