English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The convergence of solutions of the incompressible Navier-Stokes equationsset in a domain with boundary to solutions of the Euler equations in the largeReynolds number limit is a challenging open problem both in 2 and 3 spacedimensions. In particular it is distinct from the question of existence in thelarge of a smooth solution of the initial-boundary value problem for the Eulerequations. The present paper proposes three results in that direction. First,if the solutions of the Navier-Stokes equations satisfy a slip boundarycondition with vanishing slip coefficient in the large Reynolds number limit,we show by an energy method that they converge to the classical solution of theEuler equations on its time interval of existence. Next we show that theincompressible Navier-Stokes limit of the Boltzmann equation with Maxwell'saccommodation condition at the boundary is governed by the Navier-Stokesequations with slip boundary condition, and we express the slip coefficient atthe fluid level in terms of the accommodation parameter at the kinetic level.This second result is formal, in the style of [Bardos-Golse-Levermore, J. Stat.Phys. 63 (1991), 323-344]. Finally, we establish the incompressible Euler limitof the Boltzmann equation set in a domain with boundary with Maxwell'saccommodation condition assuming that the accommodation parameter is smallenough in terms of the Knudsen number. Our proof uses the relative entropymethod following closely the analysis in [L. Saint-Raymond, Arch. Ration. Mech.Anal. 166 (2003), 47-80] in the case of the 3-torus, except for the boundaryterms, which require special treatment.

The Incompressible Euler Limit of the Boltzmann Equation with Accommodation Boundary Condition