Abstract
In this paper we consider some dissipative versions of the modified Korteweg--de~Vries equation $u_t+u_{xxx}+|D_x|^{\alpha}u+u^2u_x=0$ with $0 <\alpha\leq 3$. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces $H^s({ \mathbb R})$ for $s>1/4-\alpha/4$ on the basis of the $[k;\,Z]-$multiplier norm estimate obtained by Tao in [11] for KdV equation.
Citation
Wengu Chen. Junfeng Li. Changxing Miao. "On the well-posedness of the Cauchy problem for dissipative modified Korteweg-de Vries equations." Differential Integral Equations 20 (11) 1285 - 1301, 2007. https://doi.org/10.57262/die/1356039289
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