Event Type:

Analysis Seminar

Date/Time:

Monday, April 21, 2014 - 05:00

Location:

Kidder 280

Local Speaker:

Abstract:

Solutions of the Euler equations, while smooth, should conserve energy (defined as the L^2 norm of the velocity field.) In a recent paper by Camillo De Lellis and Laszlo Szekelyhide (Inventiones Mathematicae 2013) the authors show the existence of solutions of the Euler equations in the sense of distributions that have a prescribed, strictly positive, energy profile e(t). The construction of these solutions is obtained using an iteration scheme in which Bernoulli flows play a fundamental role. I will survey these results with a major emphasis on illustrating the importance of Bernoulli flows, which are classical steady state solutions of the Euler equations. The dissipation of energy is due to the prescence of faster oscillations in the approximate solutions.