These are a series of lectures given at the 1997 Cattedra Galileiana, at Scuola Normale Superiore. We discuss in these notes two mathematical topics related to Euler equations and turbulence. The gene
Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding
One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no c
Not a comprehensive treatment but a selection of the most significant mathematical results on fluid mechanics models. Limited to newtonian liquids. Describes density-dependent and other Navier-Stokes
This volume and its companion, both written by a winner of the 1994 Fields Medal, provide a unique and rigorous treatise on mathematical aspects of fluid mechanics models. These models consist of syst
This volume has resulted from an IMA workshop that sought to provide a mix of topics from both traditional areas of stochastic control theory and newer areas of application. The papers represent a div
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribut
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribut