Paper

Low Mach number limit on thin domains

, , and

Published 10 January 2020 • © 2020 IOP Publishing Ltd & London Mathematical Society
, , Citation Matteo Caggio et al 2020 Nonlinearity 33 840 DOI 10.1088/1361-6544/ab52df

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Author e-mails

matteo.caggio@univaq.it

donatella.donatelli@univaq.it

matus@math.cas.cz

sunyz@nju.edu.cn

Author affiliations

1 Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy

2 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic

3 Department of Mathematics, Nanjing University, Nanjing, People's Republic of China

Dates

  1. Received 27 January 2019
  2. Accepted 30 October 2019
  3. Published

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0951-7715/33/2/840

Abstract

We consider the compressible Navier–Stokes system describing the motion of a viscous fluid confined to a straight layer . We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier–Stokes equations (Euler equations) when the Mach number tends to zero as well as (and the viscosity goes to zero).

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10.1088/1361-6544/ab52df