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

作者：Wu Gang^*; Yuan Ha

来源：Journal of Mathematical Analysis and Applications, 2008, 340(2): 1326-1335.

DOI：10.1016/j.jmaa.2007.09.060

• dissipative equation
• Cauchy problem
• well-posedness
• Besov spaces
• Fourier localization
• Littlewood-Paley theory

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.

• 出版日期2008-4-15
• 单位中国工程物理研究院