Osaka Journal of Mathematics

Ill-posedness issue for the drift diffusion system in the homogeneous Besov spaces

Tsukasa Iwabuchi and Takayoshi Ogawa

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Abstract

We consider the ill-posedness issue for the drift-diffusion system of bipolar type by showing that the continuous dependence on initial data does not hold generally in the scaling invariant Besov spaces. The scaling invariant Besov spaces are $\dot{B}_{p, \sigma}^{-2+ n/p} (\mathbb{R}^{n})$ with $1 \leq p, \sigma \leq \infty$ and we show the optimality of the case $p = 2n$ to obtain the well-posedness and the ill-posedness for the drift-diffusion system of bipolar type.

Article information

Source
Osaka J. Math. Volume 53, Number 4 (2016), 919-939.

Dates
First available in Project Euclid: 4 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1475601824

Mathematical Reviews number (MathSciNet)
MR3554849

Zentralblatt MATH identifier
06654656

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K08: Heat kernel

Citation

Iwabuchi, Tsukasa; Ogawa, Takayoshi. Ill-posedness issue for the drift diffusion system in the homogeneous Besov spaces. Osaka J. Math. 53 (2016), no. 4, 919--939. https://projecteuclid.org/euclid.ojm/1475601824.


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