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Register a new user$L^2$-stableness for solution to linearized KdV equation
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The linearized Korteweg-De Vries equation can be written as a Hamilton-like system. However, the Hamilton energy depends on the time, and is a nonsymmetric operator on $L^2({bf R})$. By performing suitable unitary transforms on the Hamilton energy, we can reduce this operator into one that is not independent on the time but nonsymmetric. In this study, we consider the $L^2$-stability issues and smoothing estimates for this operator, and prove that it has no eigenvalues.
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We prove local-wellposedness of the mKdV equation in $mathcal{F}L^{s,p}$ spaces using the new method of M. Christ.
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