Existence of Solutions for the Debye-Hckel System with Low Regularity Initial Data
In this paper we study existence of solutions for the Cauchy problem of the Debye-Hckel 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 \(-\frac{3}{2}<s\leq-2+\frac{n}{2}\), \(p=\frac{n}{s+2}\) and 1?q??, and furthermore, if the initial data is sufficiently small then the solution is global. This result improves the regularity index of the initial data space in previous results on this system. The blow-up criterion of solutions is also established.
debye-hckel system low regularity global existence blow up 35k45 35q99