Inviscid limit for no-slip boundary conditions

Establish whether the incompressible Navier–Stokes solutions converge to the corresponding incompressible Euler solutions in the vanishing-viscosity limit under no-slip boundary conditions on a bounded domain, without additional assumptions such as energy-dissipation bounds, analyticity, or symmetry.

Background

The paper studies the validity and breakdown of the inviscid approximation, primarily for flows on the two-dimensional torus. In the bounded-domain setting, the authors distinguish Navier boundary conditions, for which unconditional inviscid-limit results are available, from no-slip boundary conditions, for which the general convergence problem remains unresolved.

The unresolved issue concerns whether viscous Navier–Stokes flows with no-slip boundaries approach the corresponding Euler flow as viscosity tends to zero, absent supplementary structural or dissipation hypotheses. The paper notes that lower bounds on the separation time can nevertheless be established in periodic channels and general smooth domains.