一类抛物方程在Fourier-Besov-Morrey空间内解的适定性

The Well-Posedness of Solutions to a Class of Parabolic Equations in Fourier-Besov-Morrey Spaces

摘要: 本文应用傅里叶局部化方法和Littlewood-Paley定理，在临界Fourier-Besov-Morrey空间$ℱ{\dot{\mathcal{N}}}_{p,\lambda ,q}^s\left({ℝ}^3\right)$ 对一类抛物方程小初值解的全局适定性问题进行研究，其中$s=2-2\alpha +\frac{3}{p^{\prime }}+\frac{\lambda }{p}$ 。

Abstract: This paper applies the Fourier localization method and the Littlewood-Paley theorem to study the global well-posedness of small initial value solutions for a class of parabolic equations in the critical Fourier-Besov-Morrey spaces $ℱ{\dot{\mathcal{N}}}_{p,\lambda ,q}^s\left({ℝ}^3\right)$ where $s=2-2\alpha +\frac{3}{p^{\prime }}+\frac{\lambda }{p}$ .