Sharp ill-posedness results for the KdV and mKdV equations on the torus
نویسنده
چکیده
We establish a new a priori bound for L-bounded sequences of solutions to the mKdV equations on the torus. This first enables us to construct weak solutions in L for this equation and to check that the ”solutions” constructed by Kappeler and Topalov in the defocusing case satisfy the equation in some weak sense. In a second time, we prove that the solution-map associated with the mKdV and the KdV equation are discontinuous for the Hs(T) topology for respectively s < 0 and s < −1. These last results are sharp.
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