Emergence of Peaked Singularities in the Euler–Poisson System
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DOI: 10.1007/s00332-024-10119-2
Abstract: We consider the one-dimensional Euler–Poisson system equipped with the Boltzmann relation and provide the exact asymptotic behavior of the peaked solitary wave solutions near the peak. This enables us to study the cold ion limit… read more here.
Keywords: euler poisson; poisson system; peaked solitary; usepackage ... See more keywords
Exact solutions to 2D isothermal Euler-Poisson equations with qualitative analysis
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DOI: 10.1016/j.cjph.2020.07.005
Abstract: Abstract The family of exact solutions with parameter λ of the 2D isothermal Euler-Poisson equations, which can be used to model the evolution of self-gravitating galaxies or gaseous stars, is investigated. By solving the Liouville… read more here.
Keywords: energy; isothermal euler; poisson equations; exact solutions ... See more keywords
Quasi-neutral limit for Euler-Poisson system in the presence of boundary layers in an annular domain
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.06.011
Abstract: Abstract We investigate the quasi-neutral limit (the zero Debye length limit) for the Euler-Poisson system with radial symmetry in an annular domain. Under physically relevant conditions at the boundary, referred to as the Bohm criterion,… read more here.
Keywords: poisson system; neutral limit; limit; limit euler ... See more keywords
Global solutions to compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma on exterior domains
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.07.005
Abstract: Abstract The initial boundary value problems for compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma are considered on exterior domains in this paper. With the radial symmetry assumption, the global existence of solutions to compressible Navier-Stokes-Poisson… read more here.
Keywords: compressible navier; stokes poisson; poisson euler; poisson equations ... See more keywords
Derivation of the mKdV equation from the Euler-Poisson system at critical densities
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DOI: 10.1016/j.jde.2021.02.026
Abstract: Abstract In this paper, we consider the long wavelength limit for the Euler-Poisson system arising in plasma including three species. It is demonstrated that when the plasma has critical densities, the modified Korteweg-de Vries (mKdV)… read more here.
Keywords: euler poisson; mkdv equation; poisson system;
Small data solutions for the Euler-Poisson-Darboux equation with a power nonlinearity
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2021.03.033
Abstract: Abstract We study the Cauchy problem for the Euler-Poisson-Darboux equation, with a power nonlinearity: u t t − u x x + μ t u t = t α | u | p , t… read more here.
Keywords: euler poisson; small data; poisson darboux; power ... See more keywords
On the regularity of the solution map of the Euler-Poisson system
Sign Up to like & getrecommendations! Published in 2019 at "TURKISH JOURNAL OF MATHEMATICS"
DOI: 10.3906/mat-1806-76
Abstract: In this paper we consider the Euler-Poisson system (describing a plasma made of ions with a negligible ion temperature) on the Sobolev spaces $H^s(\R^3)$, $s > 5/2$. Using a geometric approach we show that for… read more here.
Keywords: poisson system; solution map; euler poisson;
Stationary solution to stochastically forced Euler-Poisson equations in bounded domain: Part 1. 3-D insulating boundary
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DOI: 10.3934/dcds.2025041
Abstract: This paper is concerned with $3$-D stochastic Euler-Poisson equations with insulating boundary conditions forced by the Wiener process. We first establish the global existence and uniqueness of the solution to the system, then we prove… read more here.
Keywords: euler poisson; insulating boundary; solution; poisson equations ... See more keywords