带有分数扩散的多维Burgers方程的衰减估计

Abstract

Abstract:

In this paper, we investigate the time decay properties of the global weak solutions to the multi-dimensional Burgers' equation with fractional diffusion. We establish the optimal decay rates in L² or L^p norm to solutions with initial data u₀∈L²∩L^p for p≠2. If u₀∈L² only, we also show that it is impossible to obtain a uniform decay. Finally, for u₀∈L²∩L^n/2α-1, we obtain a uniform decay estimate of solutions in L^p norm for any p>n/2α-1.

Key words: Fractional Burgers' equation, Large initial data, Optimal decay rate

CLC Number:

O175.29

Yu Pei. Decay of Weak Solutions to the Multi-Dimensional Burgers' Equation with Fractional Diffusion[J].Acta mathematica scientia,Series A, 2016, 36(2): 340-352.

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Decay of Weak Solutions to the Multi-Dimensional Burgers' Equation with Fractional Diffusion

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