Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik: (Ams-219) (Annals of Mathematics Studies #215) (Paperback)

Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik: (Ams-219) (Annals of Mathematics Studies #215) By Camillo De Lellis, Elia Brué, Dallas Albritton Cover Image
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An essential companion to M. Vishik's groundbreaking work in fluid mechanics

The incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich from the 1960s, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich's theorem cannot be generalized to the L p setting.
Product Details
ISBN: 9780691257532
ISBN-10: 0691257531
Publisher: Princeton University Press
Publication Date: February 13th, 2024
Pages: 148
Language: English
Series: Annals of Mathematics Studies