TRANSPORT EQUATIONS WITH UNBOUNDED FORCE FIELDS AND APPLICATION TO THE VLASOV–POISSON EQUATION

DOI10.1142/S0218202509003401zbMath1165.82011MaRDI QIDQ3620379

Delphine Salort

Publication date: 14 April 2009

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Vlasov-Poisson equationdispersion estimate

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Initial value problems for linear first-order PDEs (35F10) Dispersion theory, dispersion relations arising in quantum theory (81U30)

Related Items (14)

Global existence to the Vlasov-Poisson system and propagation of moments without assumption of finite kinetic energy ⋮ The Vlasov-Poisson system with low steady spatial asymptotics ⋮ On stationary solutions of the Vlasov-Poisson equations ⋮ Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system ⋮ On the magnetic shield for a Vlasov-Poisson plasma ⋮ On global solutions to the Vlasov-Poisson system with radiation damping ⋮ Classical solutions for the Vlasov–Poisson system with damping term ⋮ A uniqueness criterion for unbounded solutions to the Vlasov-Poisson system ⋮ The two dimensional Vlasov-Poisson system with steady spatial asymptotics ⋮ Ion energization by wave-particle interactions: comparison of spectral and particle simulation solutions of the Vlasov equation ⋮ On the Attractive Plasma-Charge System in 2-d ⋮ Moment Propagation for Weak Solutions to the Vlasov–Poisson System ⋮ Global existence and propagation of moments for a Vlasov-Poisson equation with a point charge ⋮ Polynomial propagation of moments and global existence for a Vlasov-Poisson system with a point charge

Cites Work

• Uniqueness of the solution to the Vlasov--Poisson system with bounded density
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• Propagation of space moments in the Vlasov-Poisson equation and further results
• Regularity and propagation of moments in some nonlinear Vlasov systems
• Weak solutions of the initial value problem for the unmodified non‐linear vlasov equation
• On the classical solutions of the initial value problem for the unmodified non‐linear Vlasov equation I general theory
• On the classical solutions of the initial value problem for the unmodified non‐linear vlasov equation II special cases
• Global existence of smooth solutions to the vlasov poisson system in three dimensions
• Mathematical tools for kinetic equations
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Equations d'ondes quasilineaires et estimations de Strichartz
• Dispersion and Strichartz estimates for the Liouville equation

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