时 间: 2022-01-13 11:30 — 12:30
Consider the steady solution to the incompressible Euler equation Ae1 in the periodic tunnel Ω = [0, 1] × T2 . Consider now the family of solutions Uν to the associated Navier-Stokes equation with no-slip condition on the flat boundaries, for small viscosities ν = 1/Re, and initial values close in L2 to Ae1. Under a conditional assumption on the energy dissipation close to the boundary, Kato showed in 1984 that Uν converges to Ae1 when the viscosity converges to 0 and the initial value converge to Ae1. It is still unknown whether this inviscid is unc onditionally true. Actually, the convex integration method predicts the possibility of a layer separation. It produces solutions to the Euler equation with initial values Ae1, but with layer separation energy at time T up to: