Nonlinear instability in Vlasov type equations around rough velocity profiles

DOI10.1016/j.anihpc.2019.12.002zbMath1441.35234arXiv1811.01350OpenAlexW2999121634MaRDI QIDQ2179475

Aymeric Baradat

Publication date: 12 May 2020

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01350

zbMATH Keywords

measure-valued solutionsVlasov-Poissonnonlinear instabilityPenrose condition

Mathematics Subject Classification ID

Statistical mechanics of plasmas (82D10) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Vlasov equations (35Q83) Euler equations (35Q31) PDEs with measure (35R06)

Related Items

The non-relativistic limit of the Vlasov-Maxwell system with uniform macroscopic bounds ⋮ On the Existence of a Scalar Pressure Field in the Brödinger Problem ⋮ Recent developments on quasineutral limits for Vlasov-type equations ⋮ Various formulations and approximations of incompressible fluid motions in porous media

Cites Work

• The dual least action problem for an ideal, incompressible fluid
• Uniqueness of the solution to the Vlasov--Poisson system with bounded density
• Geodesics in the space of measure-preserving maps and plans
• Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• On classical solutions in the large in time of two-dimensional Vlasov's equation
• A homogenized model for vortex sheets
• Two-stream instabilities in plasmas
• Continuous dependence of the pressure field with respect to endpoints for ideal incompressible fluids
• Nonlinear instability of double-humped equilibria
• Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation
• About a variant of the \(1d\) Vlasov equation, dubbed ``Vlasov-Dirac-Benney equation
• The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Ill-posedness of the hydrostatic Euler and singular Vlasov equations
• Hamiltonian Structure, Fluid Representation and Stability for the Vlasov–Dirac–Benney Equation
• Nonlinear Instability of Vlasov--Maxwell Systems in the Classical and Quasineutral Limits
• A Vlasov equation with Dirac potential used in fusion plasmas
• Quasineutral limit for Vlasov-Poisson with Penrose stable data
• Quasineutral Limit of the Vlasov-Poisson System with Massless Electrons
• A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities
• Electrostatic Instabilities of a Uniform Non-Maxwellian Plasma
• The Least Action Principle and the Related Concept of Generalized Flows for Incompressible Perfect Fluids
• Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
• Editorial board
• Oscillations in quasineutral plasmas
• Topological Methods in Hydrodynamics
• Unnamed Item
• Unnamed Item