Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations

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Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws (2015, methodology): “Applications of the relative entropy method in this context began with the work of Yau [55] and have been studied in various context (See for instance [2, 3, 7, 8, 23, 26, 34, 37, 38, 42]).”
GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS (2007, background): “In its most general form, the reflection operator B can be written as Bf(v) = ∫ v′·n>0 B(t, x, v, v′)f(v′) |v′ · r(x)|dv′ The usual assumptions on the kernel B are the following: (i) The operator B is non-negative (i.e.”
Global Solutions to the Coupled Chemotaxis-Fluid Equations (2010, methodology): “For that, refer to [3, 6, 13, 14, 16, 25, 26] for the study of the Vlasov–Fokker–Planck equation coupled with the compressible or incompressible Navier–Stokes or Stokes equations, where the main tool used to prove the global existence of weak solutions or hydrodynamical limit is the existing entropy”
Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations (2010, background): “For the compressible limit, see Tzavaras [40] in the context of relaxation and [4, 3, 33] in the context of hydrodynamical limits.”