Differential and Integral Equations
- Differential Integral Equations
- Volume 28, Number 7/8 (2015), 753-776.
Two dimensional drift-diffusion system in a critical weighted space
We establish the time local well-posedness of a multi-component parabolic-elliptic drift-diffusion model in two space dimensions in a scaling critical weighted space. This is a generalization of former result Kurokiba-Ogawa  and corresponds to the critical case for multiple system treated in Kurokiba . In order to show the critical well-posedness, we introduce a refined version of Brezis-Gallouët inequality in term of the Besov space and apply it to the some weighted estimate in two dimensions.
Differential Integral Equations, Volume 28, Number 7/8 (2015), 753-776.
First available in Project Euclid: 11 May 2015
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 35Q60: PDEs in connection with optics and electromagnetic theory 78A35: Motion of charged particles
Kurokiba, Masaki; Ogawa, Takayoshi. Two dimensional drift-diffusion system in a critical weighted space. Differential Integral Equations 28 (2015), no. 7/8, 753--776. https://projecteuclid.org/euclid.die/1431347862