Well-posedness of the Cauchy problem for the fractional power dissipative equation in critical Besov spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:340

Article

Wu, Gang¹  Yuan, Ha¹ 

[1] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China

关键词: dissipative equation;    Cauchy problem;    well-posedness;    Besov spaces;    Fourier localization;    Littlewood-Paley theory;   

DOI  :  10.1016/j.jmaa.2007.09.060

来源: Elsevier

【 摘 要 】

In this paper we study the Cauchy problem for the semilinear fractional power dissipative equation u(t) + (-Delta)(alpha)u = F(u) for the initial data u(0) in critical Besov spaces B-2,r(sigma) with sigma ((Delta)) double under bar n/2 - 2 alpha-d/b, where alpha > 0, F(u) = P(D)u(b+1) with P(D) being a homogeneous pseudo-differential operator of order d E [0, 2ot) and b > 0 being an integer. Making use of some estimates of the corresponding linear equation in the frame of mixed time-space spaces, the so-called. mono-norm method which is different from the Kato's double-norm method, Fourier localization technique and Littlewood-Paley theory, we get the well-posedness result in the case sigma > - n/2. (c) 2007 Elsevier Inc. All rights reserved.

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