1. Long time existence of smooth solutions to 2D Euler-Poisson system of electrons with non-zero vorticity.
- Author
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Shiyu, Li and Huicheng, Yin
- Subjects
- *
SOBOLEV spaces , *VORTEX motion , *ELECTRONS , *VELOCITY , *DENSITY , *CLASSICAL solutions (Mathematics) - Abstract
In this paper, we investigate the long time existence of the classical solution to 2D one-fluid Euler-Poisson system of electrons with non-zero vorticity in the standard Sobolev spaces so that both the local solution and long time solution lie in the same Sobolev space framework without any extra restrictions of space-decay rates at infinity. It is shown that the lifespan of the classical solution is at least T ε , δ = min { e ε − 2 | l n ε | − α , κ δ } , where ε > 0 is the size of the initial perturbed density and velocity, δ > 0 is the size of the initial vorticity, α > 0 is any fixed number, κ > 0 is a suitable constant. We decompose the Euler-Poisson system into three bilinear interaction parts: dispersion–dispersion, vorticity–dispersion, and vorticity–vorticity. Based on the Strichartz inequality, the related quartic energy estimates, the conservation of specific vorticity along the streamline and some delicate analysis, the precise bound of lifespan T ε , δ is obtained. By the way, for the 2D irrotational one-fluid Euler-Poisson system with small amplitude ε of the perturbed initial data in the Sobolev spaces, we obtain an interesting long time existence result with lifespan T ε ≥ e ε − 2 | l n ε | − α (α > 0 is any fixed constant). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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