Existence of Solutions for the Debye-Hückel System with Low Regularity Initial Data

Details Existence of Solutions for the Debye-Hückel System with Low Regularity Initial Data Existence of Solutions for the Debye-Hückel System with Low Regularity Initial Data

2011-05-19

arxiv.org/abs/1105.3844v1

Mathematics

Analysis of PDEs

9 pages

Scientific paper

In this paper we study existence of solutions for the Cauchy problem of the Debye-H\"{u}ckel system with low regularity initial data. By using the Chemin-Lerner time-space estimate for the heat equation, we prove that there exists a unique local solution if the initial data belongs to the Besov space $\dot{B}^{s}_{p,q}(\mathbb{R}^{n})$ for $-3/2

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