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Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains.
- Source :
-
Transactions of the American Mathematical Society . Nov2021, Vol. 374 Issue 11, p7867-7924. 58p. - Publication Year :
- 2021
-
Abstract
- It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity coefficients of order of the Knudsen number ε >0. In the paper, we carry out the rigorous mathematical analysis of the compressible Navier-Stokes approximation for the Boltzmann equation regarding the initial-boundary value problems in general bounded domains. The main goal is to measure the uniform-in-time deviation of the Boltzmann solution with diffusive reflection boundary condition from a local Maxwellian with its fluid quantities given by the solutions to the corresponding compressible Navier-Stokes equations with consistent non-slip boundary conditions whenever ε > 0 is small enough. Specifically, it is shown that for well chosen initial data around constant equilibrium states, the deviation weighted by a velocity function is O(ε1/2) in L∞x,v and O(ε3/2) in L2x,v globally in time. The proof is based on the uniform estimates for the remainder in different functional spaces without any spatial regularity. One key step is to obtain the global-in-time existence as well as uniform-in-ε estimates for regular solutions to the full compressible Navier-Stokes equations in bounded domains when the parameter ε > 0 is involved in the analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 153120694
- Full Text :
- https://doi.org/10.1090/tran/8437