Incompressible Navier-Stokes-Fourier limit from the Landau equation

Mohamad Rachid (1, 2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 UN UFR ST - Université de Nantes - UFR des Sciences et des Techniques

In this work, we study the Landau equation, depending on the Knudsen Number and its limit to the incompressible Navier-Stokes-Fourier equation on the torus. We prove uniform estimate of some adapted Sobolev norm and get existence and uniqueness of solution for small data. These estimates are uniform in the Knudsen number and allow to derive the incompressible Navier-Stokes-Fourier equation when the Knudsen number tends to 0.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Mathématiques générales [math.GM]; Analyse fonctionnelle [math.FA]; Analyse numérique [math.NA]

Mohamad Rachid. Incompressible Navier-Stokes-Fourier limit from the Landau equation. Kinetic and Related Models , 2021, 14 (4), pp.599-638. ⟨10.3934/krm.2021017⟩. ⟨hal-03035871v2⟩