Abstract
In this paper, we study the hydrodynamic limit to contact discontinuity of the compressible Euler system for the Landau equation with the physical Coulomb interaction as the Knudsen number ε>0 is vanishing. Our results are twofold. First, we construct the unique global-in-time solution to the Landau equation with suitably small initial data as ε>0 is sufficiently small. Second, we prove that the solution of the Landau equation converges to a local Maxwellian whose fluid quantities are the contact discontinuity of the corresponding Euler system uniformly away from the discontinuity as ε→0. Moreover, the uniform convergence rate is also obtained. The main idea is to introduce a new time-velocity weigh function to induce an extra quartic dissipation term for treating the large-velocity growth in the nonlinear estimates due to degeneration of the linearized Landau operator in the Coulomb case.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
