Title: Geometric and analytic methods in fluid dynamics
Speaker: Feride Tiglay
Abstract:
Abstract: The Euler equations of ideal hydrodynamics is a geodesic equation with respect to the right invariant $L^2$ metric on the group of volume preserving diffeomorphisms [1]. Arnold’s approach inspired a novel method for establishing well-posedness in the sense of Hadamard for the Cauchy problem for Euler equations [2]. This intriguing geometric-analytic framework has been developed further on Lie groups (transformation groups) to include more PDE with deep connections to mathematical physics. We will outline this framework and cover the latest developments on the analysis of PDE.
References :
[1] V. Arnold. Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits. Annales de l’Institut Fourier, 16(1):319–361, 1966.
[2] D. G. Ebin and J. Marsden. Groups of diffeomorphisms and the motion of an incompressible fluid. Annals of Mathematics, 92(1):102–163, 1970.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Nimish Shah.
