On the Cauchy problem for the fractional drift-diffusion system in critical Besov spaces

Abstract

In this paper, we establish global well-posedness and asymptotic stability of mild solutions for the Cauchy problem of the fractional drift-diffusion system with small initial data in critical Besov spaces. The regularizing-decay rate estimates of mild solutions are also proved, which imply that mild solutions are analytic in space variables.

Keywords:

• fractional drift-diffusion system
• Cauchy problem
• mild solutions
• Besov spaces

AMS Subject Classifications:

• 35C06
• 35R11
• 76W05

Acknowledgments

The authors are glad to thank the referees for their helpful comments and suggestions.