Direct dynamical energy cascade in the modified KdV equation
نویسندگان
چکیده
منابع مشابه
An Improved Local Wellposedness Result for the Modified Kdv-equation
The Cauchy problem for the modified KdV-equation ut + uxxx = (u 3)x, u(0) = u0 is shown to be locally wellposed for data u0 in the space Ĥr s (R) defined by the norm ‖u0‖ Ĥr s := ‖〈ξ〉sû0‖Lr′ ξ , provided 4 3 < r ≤ 2, s ≥ 1 2 − 1 2r . For r = 2 this coincides with the best possible result on the H-scale due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the Fourier restrictio...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2015
ISSN: 0167-2789
DOI: 10.1016/j.physd.2015.01.002