The well-posedness of Cauchy problem for dissipative modified Korteweg de Vries equations
Wengu Chen, Junfeng Li, Changxing Miao
Abstract
In this paper we consider some dissipative versions of the modified Korteweg de Vries equation ut+uxxx+|Dx|αu+u2ux=0 with 0<α≤ 3. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces Hs( R) for s>1/4-α/4 on the basis of the [k; Z]-multiplier norm estimate obtained by Tao in Tao for KdV equation.
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