2023/08/07 by Junsik Bae, Bae, Junsik, Daisuke Kawagoe +1
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing
paper · doi:10.48550/arxiv.2308.03410
openalex publication_date 2023/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the nonexistence of multi-dimensional solitary waves for the Euler-Poisson system governing ion dynamics. It is well-known that the one-dimensional Euler-Poisson system has solitary waves that travel faster than the ion-sound speed. In contrast, we show that the two-dimensional and three-dimensional models do not admit nontrivial irrotational spatially localized traveling waves for any traveling velocity and for general pressure laws. We derive some Pohozaev type identities associated with the energy and density integrals. This approach is extended to prove the nonexistence of irrotational multi-dimensional solitary waves for the two-species Euler-Poisson system for ions and electrons.