The incompressible Navier-Stokes-Fourier limit from Boltzmann-Fermi-Dirac equation

DOI10.1016/j.jde.2021.10.061zbMath1478.35164arXiv2102.02656OpenAlexW3213164139MaRDI QIDQ2054011

Yanyan Li

Publication date: 30 November 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.02656

zbMATH Keywords

classical solutionBoltzmann-Fermi-Dirac equationNavier-Stokes-Fourier limit

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Related Items (2)

Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials ⋮ The compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi-Dirac statistics

Cites Work

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• Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
• From Newton to Boltzmann: hard spheres and short-range potentials
• Optimal time decay of the quantum Landau equation in the whole space
• From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate
• Regularity of the Boltzmann equation in convex domains
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• Decay and continuity of the Boltzmann equation in bounded domains
• Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions
• On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: global existence of weak solutions
• Existence and conservation laws for the Boltzmann-Fermi-Dirac equation in a general domain
• Acoustic limit of the Boltzmann equation: classical solutions
• Local Hilbert expansion for the Boltzmann equation
• The Boltzmann equation and its applications
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• Kinetic models and quantum effects: A modified Boltzmann equation for Fermi-Dirac particles
• On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• Compactness in Boltzmann's equation via Fourier integral operators and applications. III
• Asymptotic description of Dirac mass formation in kinetic equations for quantum particles
• On the quantum Boltzmann equation
• On the quantum Boltzmann equation near Maxwellian and vacuum
• A numerical scheme for the quantum Boltzmann equation with stiff collision terms
• THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
• Global classical solutions of the Boltzmann equation without angular cut-off
• ON THE WEAK-COUPLING LIMIT FOR BOSONS AND FERMIONS
• Acoustic limit for the Boltzmann equation in optimal scaling
• The fluid dynamic limit of the nonlinear boltzmann equation
• THE CLASSICAL INCOMPRESSIBLE NAVIER-STOKES LIMIT OF THE BOLTZMANN EQUATION
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Time evolution of large classical systems
• Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• The Boltzmann equation in the whole space
• Diffusive Limit of the Boltzmann Equation with Fluid Initial Layer in the Periodic Domain
• Boltzmann diffusive limit beyond the Navier‐Stokes approximation
• The Euler limit for kinetic models with Fermi–Dirac statistics
• On some related non homogeneous 3D Boltzmann models in the non cutoff case
• On spatially homogeneous solutions of a modified Boltzmann equation for Fermi-Dirac particles.

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