On the Well Posedness of the Modified Korteweg-de Vries Equation in Weighted Sobolev Spaces
نویسنده
چکیده
We study local and global well posedness of the k-generalized Korteweg-de Vries equation in weighted Sobolev spaces Hs(R) ∩ L2(|x|2rdx).
منابع مشابه
The well - posedness of Cauchy problem for dissipative modified Korteweg de Vries equations ∗
Abstract. In this paper we consider some dissipative versions of the modified Korteweg de Vries equation ut+uxxx+ |Dx| u+uux = 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 [9] for KdV equation. 2000 Mathematics Subject Classification: 35Q5...
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