The Optimal Temporal Decay Estimates for the Fractional Power Dissipative Equation in Negative Besov Spaces

Abstract

In this paper, we first generalize a new energy approach, developed by Y. Guo and Y. Wang \cite{GW12}, in the framework of homogeneous Besov spaces for proving the optimal temporal decay rates of solutions to the fractional power dissipative equation, then we apply this approach to the supercritical and critical quasi-geostrophic equation and the critical Keller-Segel system. We show that the negative Besov norm of solutions is preserved along time evolution, and obtain the optimal temporal decay rates of the spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

23 pages. arXiv admin note: text overlap with arXiv:1508.02023

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• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
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Cited by in corpus (1)

• On a drift-diffusion system for semiconductor devices