Schrödinger‐Poisson system with Hardy‐Littlewood‐Sobolev critical exponent
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5694
Abstract: In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where parameters α,β∈(0,3),λ>0, Aα=Γ(3−α2)2απ32Γ(α2) , 2α∗=3+α , and 2β∗=3+β are the Hardy‐Littlewood‐Sobolev critical exponents. For α0, we prove the existence of nonnegative groundstate solution to… read more here.
Keywords: dinger poisson; system; hardy littlewood; littlewood sobolev ... See more keywords
Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities
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DOI: 10.1002/mma.6019
Abstract: In this paper, we are concerned with a class of fractional Schrödinger‐Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions. read more here.
Keywords: dinger poisson; fractional schr; critical nonlinearities; poisson system ... See more keywords
On the Linearized Vlasov–Poisson System on the Whole Space Around Stable Homogeneous Equilibria
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DOI: 10.1007/s00220-021-04228-2
Abstract: We study the linearized Vlasov-Poisson system around suitably stable homogeneous equilibria on $\mathbb{R}^d\times \mathbb{R}^d$ (for any $d \geq 1$) and establish dispersive $L^\infty$ decay estimates in the physical space. read more here.
Keywords: poisson system; linearized vlasov; homogeneous equilibria; stable homogeneous ... See more keywords
Asymptotic growth bounds for the Vlasov-Poisson system with radiation damping
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DOI: 10.1007/s10473-022-0104-1
Abstract: We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions. For any smooth solution with compact support, we prove a sub-linear growth estimate of its velocity support. As a consequence,… read more here.
Keywords: vlasov poisson; system radiation; poisson system; radiation damping ... See more keywords
Observers of Vlasov-Poisson system
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DOI: 10.1016/j.ifacol.2020.12.1647
Abstract: Abstract This work focuses on observer’s for one-dimensional (1D) Vlasov-Poisson (VP) system. Thanks to the discontinuous Galerkin method (DGM) to put the system into a suitable and explicit state space representation form. Then we construct… read more here.
Keywords: system; vlasov poisson; poisson system; observers vlasov ... See more keywords
A sharp time-weighted inequality for the compressible Navier–Stokes–Poisson system in the critical L framework
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DOI: 10.1016/j.jde.2018.11.005
Abstract: Abstract The compressible Navier–Stokes–Poisson system takes the form of usual Navier–Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electrostatic potential force. In this… read more here.
Keywords: time; poisson system; sharp time; compressible navier ... See more keywords
Quasi-neutral limit for Euler-Poisson system in the presence of boundary layers in an annular domain
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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
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;
Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.07.052
Abstract: Abstract In this paper, we study the following Schrodinger-Poisson system { − Δ u + V ( x ) u + λ ϕ u = | u | 4 u + μ f ( u… read more here.
Keywords: least energy; poisson system; energy sign; sign changing ... See more keywords
FRACTIONAL SCHRÖDINGER–POISSON SYSTEM WITH SINGULARITY: EXISTENCE, UNIQUENESS, AND ASYMPTOTIC BEHAVIOR
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DOI: 10.1017/s0017089520000099
Abstract: Abstract In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*} where… read more here.
Keywords: schr dinger; dinger poisson; poisson system; system singularity ... See more keywords
On the Well-posedness of the Magnetic Schrödinger-Poisson System in ℝ3
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DOI: 10.1051/mmnp/201712102
Abstract: We prove global existence and uniqueness of strong solutions for the Schrodinger-Poisson system in the repulsive Coulomb case in ℝ3 in the presence of a smooth magnetic field. read more here.
Keywords: poisson system; poisson; well posedness; posedness magnetic ... See more keywords