The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

Abstract

The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161(2004)] for Maxwell molecules.

56 pages, LaTeX, a few typos have been corrected, a few remarks added, one uncited reference removed

Cited by in corpus (17)

• Hilbert Expansion from the Boltzmann equation to relativistic Fluids
• Hydrodynamic limit of the incompressible Navier-Stokes-Fourier-Maxwell System with Ohm's Law from the Vlasov-Maxwell-Boltzmann system: Hilbert expansion approach
• On hydrodynamic limits of the Vlasov-Navier-Stokes system
• From Vlasov-Poisson-Boltzmann system to incompressible Navier-Stokes-Fourier-Poisson system: convergence for classical solutions
• On a kinetic equation describing the behavior of a gas interacting mainly with radiation
• Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space
• Justification of Diffusion limit for the Boltzmann Equation with a non-trivial Profile
• Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty
• Fluid dynamic limit of Boltzmann equation for granular hard--spheres in a nearly elastic regime
• Kinetic-fluid boundary layers and acoustic limit for the Boltzmann equation with general Maxwell reflection boundary condition
• On the convergence from Boltzmann to Navier-Stokes-Fourier for general initial data
• Compressible Euler limit from Boltzmann equation with Maxwell reflection boundary condition in half-space
• Stability of the Maxwell-Stefan system in the diffusion asymptotics of the Boltzmann multi-species equation
• On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas
• Incompressible magnetohydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations
• The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics
• The incompressible Navier-Stokes limit from the lattice BGK Boltzmann equation