Construction of Invariant Measures for 2D Euler and Slow Growth of Sobolev Norms

Explore the construction of invariant measures for 2D Euler equations and the slow growth of Sobolev norms in this analysis seminar talk. Delve into the study of global solutions with regular initial conditions on the torus, examining the potential growth of Sobolev norms. Investigate current upper bounds, including double exponential growth examples on the unit disk and exponential growth on the torus. Consider the question of generic growth for random initial data, focusing on the construction of invariant measures in highly regular Sobolev spaces. Learn about the application of Bourgain's globalization argument to create slowly growing solutions. Examine the challenges in constructing invariant measures, including Kuksin's approach and the open question of studying their support.