## SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

**Minjie JIANG;Wei YAN;Yimin ZHANG;College of Mathematics and Information Science, Henan Normal University;School of Science, Wuhan University of Technology;**

This current paper is devoted to the Cauchy problem for higher order dispersive equation u_t+ ?_x~(2n+1)u = ?_x(u?_x~nu) + ?_x~(n-1)(u_x~2), n ≥ 2, n ∈ N~+.By using Besov-type spaces, we prove that the associated problem is locally well-posed in H~(-n/2+3/4,-1/(2n))(R). The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H~(s,a)(R) with s -n/2+3/4 and all a∈R.

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【Fund】： supported by Natural Science Foundation of China NSFC(11401180 and 11471330);; supported by the Young Core Teachers Program of Henan Normal University(15A110033);; supported by the Fundamental Research Funds for the Central Universities(WUT:2017 IVA 075)

【CateGory Index】： O175

**Cauchy problem****sharp well-posedness****modified Bourgain spaces**【Fund】： supported by Natural Science Foundation of China NSFC(11401180 and 11471330);; supported by the Young Core Teachers Program of Henan Normal University(15A110033);; supported by the Fundamental Research Funds for the Central Universities(WUT:2017 IVA 075)

【CateGory Index】： O175

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