This volume brings together four contributions to mathematical fluid mechanics, a classical but still highly active research field. The contributions cover not only the classical Navier-Stokes equations and Euler equations, but also some simplified models, and fluids interacting with elastic walls. The questions addressed in the lectures range from the basic problems of existence/blow-up of weak and more regular solutions, to modeling and aspects related to numerical methods.

This book covers recent advances in several important areas of fluid mechanics. An output of the CIME Summer School "Progress in mathematical fluid mechanics" held in Cetraro in 2019, it offers a collection of lecture notes prepared by T. Buckmaster, (Princeton), S. Canic (UCB) P. Constantin (Princeton) and A. Kiselev (Duke).

These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics.

Provides a concise and focused overview of selected topics in mathematical fluid mechanics Presents four lectures by leading experts in the field Covers classical material as well as modeling and connections with numerical analysis

Inhalt

• A Heuristic Approach to Convex Integration for the Euler Equations. - Fluid-Structure Interaction with Incompressible Fluids. - Regularity and Inviscid Limits in Hydrodynamic Models. - Small Scale Creation in Active Scalars.