On the Landau approximation in plasma physics.
From MaRDI portal
Publication:1426664
DOI10.1016/j.anihpc.2002.12.001zbMath1044.83007OpenAlexW1989465898MaRDI QIDQ1426664
Radjesvarane Alexandre, Cédric Villani
Publication date: 15 March 2004
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_1_61_0
Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Nonlinear first-order PDEs (35F20) Theoretical approximation in context of PDEs (35A35) Statistical mechanics of plasmas (82D10) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)
Related Items
Boltzmann to Landau from the gradient flow perspective ⋮ Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations ⋮ Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations ⋮ An \(L^2\) to \(L^\infty\) framework for the Landau equation ⋮ From the Vlasov-Poisson-Boltzmann System to the Vlasov-Poisson-Landau System with Coulomb Potential ⋮ The Vlasov-Poisson-Landau system in a periodic box ⋮ Cauchy problem and exponential stability for the inhomogeneous Landau equation ⋮ Smoothing effects for classical solutions of the full Landau equation ⋮ About the Landau-Fermi-Dirac equation with moderately soft potentials ⋮ \(H^s_{x,\nu}\) stability of the Boltzmann equation and Landau equation with soft potentials ⋮ Regularization estimates and hydrodynamical limit for the Landau equation ⋮ Global classical solutions to the initial value problem for the relativistic Landau equation ⋮ Multi-scale kinetic scheme for the collisional Vlasov-Poisson system ⋮ Entropic structure of Landau's collision kernel ⋮ Asymptotics toward viscous contact waves for solutions of the Landau equation ⋮ Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas ⋮ A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit ⋮ Landau equation for very soft and Coulomb potentials near maxwellians ⋮ Local Well-Posedness for the Boltzmann Equation with Very Soft Potential and Polynomially Decaying Initial Data ⋮ Convergence to the Landau equation from the truncated BBGKY hierarchy in the weak-coupling limit ⋮ From a non-Markovian system to the Landau equation ⋮ The 3D Vlasov-Poisson-Landau system near 1D local Maxwellians ⋮ Spectral gap and exponential convergence to equilibrium for a multi-species Landau system ⋮ Boltzmann equation with cutoff Rutherford scattering cross section near Maxwellian ⋮ L 2-stability of the Landau equation near global Maxwellians ⋮ Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff ⋮ Harnack inequality for a class of Kolmogorov-Fokker-Planck equations in non-divergence form ⋮ One-species Vlasov-Poisson-Landau system for soft potentials in ℝ3 ⋮ The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials ⋮ Entropy dissipation estimates for the Boltzmann equation without cut-off ⋮ From Boltzmann's equation to the incompressible Navier-Stokes-Fourier system with long-range interactions ⋮ Small Knudsen rate of convergence to contact wave for the Landau equation ⋮ Well-posedness of the Lenard-Balescu equation with smooth interactions ⋮ Analytic Gelfand-Shilov smoothing effect of the spatially homogeneous Landau equation with hard potentials ⋮ Singular kinetic equations and applications ⋮ Local well-posedness of the Boltzmann equation with polynomially decaying initial data ⋮ The massless electron limit of the Vlasov-Poisson-Landau system ⋮ Solutions to the non-cutoff Boltzmann equation in the grazing limit ⋮ Global \(\boldsymbol{L}_{\boldsymbol{p}}\) Estimates for Kinetic Kolmogorov–Fokker–Planck Equations in Divergence Form ⋮ Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials ⋮ Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules ⋮ Local solutions of the Landau equation with rough, slowly decaying initial data ⋮ Global smooth dynamics of a fully ionized plasma with long-range collisions ⋮ On a parabolic-parabolic system with gradient dependent chemotactic coefficient and consumption ⋮ Renormalized solutions to a chemotaxis system with consumption of chemoattractant ⋮ Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems ⋮ Interacting particle systems with long-range interactions: scaling limits and kinetic equations ⋮ Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit ⋮ The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation ⋮ Interplay of Boltzmann Equation and Continuity Equation for Accelerated Electrons in Solar Flares ⋮ On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation ⋮ Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially homogeneous case ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially inhomogeneous case ⋮ Stability of vacuum for the Landau equation with moderately soft potentials ⋮ Regularizing effect and local existence for the non-cutoff Boltzmann equation ⋮ On the Cauchy problem of the Boltzmann and Landau equations with soft potentials ⋮ Characterization of collision kernels ⋮ Small Knudsen rate of convergence to rarefaction wave for the Landau equation ⋮ The Vlasov-Poisson-Landau system in \(\mathbb{R}^{3}_{x}\) ⋮ The Vlasov-Poisson-Landau system near a local Maxwellian ⋮ One-species Vlasov-Poisson-Landau system near Maxwellians in the whole space ⋮ Some a priori estimates for the homogeneous Landau equation with soft potentials ⋮ Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation ⋮ \(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation ⋮ Entropy Dissipation Estimates for the Landau Equation: General Cross Sections ⋮ Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators ⋮ A refined estimate of the grazing limit from Boltzmann to Landau operator in Coulomb potential ⋮ The Vlasov-Maxwell-Landau system with Coulomb potential and strong background magnetic field ⋮ Entropy dissipation estimates for the Landau equation in the Coulomb case and applications ⋮ On some properties of the Landau kinetic equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the Cauchy problem for Boltzmann equations: Global existence and weak stability
- On the Fokker-Planck-Boltzmann equation
- Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
- \(L^ p\) regularity of velocity averages
- The Boltzmann equation and its applications
- On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
- On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
- Entropy dissipation and long-range interactions
- Compactness in Boltzmann's equation via Fourier integral operators and applications. III
- The Landau equation in a periodic box
- On the Cauchy problem for Landau equations: Sequential stability, global existence
- Irreversible Processes in Ionized Gases
- On asymptotics of the Boltzmann equation when the collisions become grazing
- THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE
- Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire
- Conservative forms of Boltzmann's collision operator: Landau revisited
- On Boltzmann and Landau equations
- On the Boltzmann equation for long-range interactions
- On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications
- ON THE CONNECTION BETWEEN A SOLUTION OF THE BOLTZMANN EQUATION AND A SOLUTION OF THE LANDAU-FOKKER-PLANCK EQUATION