- DONG LI, University of British Columbia
Threshold spaces for incompressible Euler equations [PDF]
The incompressible Euler equations describe the flow of an inviscid,
incompressible fluid and have very rich analytic and geometric structures.
The pioneering work of Lichtenstein, Gunther in 1940s and Kato-Ponce
in 1980s constructed solutions to the incompressible Euler
equations in function spaces above a certain regularity
threshold. The intensive research in the past several decades showed
that the complexity of the threshold cases is deeply connected with
the inherent nonlinear and non-local structures
in the Euler equations. I will survey some recent developments
on these problems.