Instability and non-uniqueness for the 2D Euler equations, after M. Vishik / Dallas Albritton, Elia Brué, Maria Colombo, Camillo De Lellis, Vikram Giri, Maximilian Janisch, Hyunju Kwon.

Format:

Book

Author/Creator:

Albritton, Dallas, author.

Brué, Elia, author.

Colombo, Maria, (Mathematician), author.

De Lellis, Camillo, author.

Giri, Vikram, author.

Janisch, Maximilian, author.

Kwon, Hyunju, author.

Series:

Annals of mathematics studies ; no. 219.

Annals of mathematics studies ; number 219

Language:

English

Subjects (All):

Fluid dynamics--Mathematical models.

Fluid dynamics.

Lagrange equations--Numerical solutions.

Lagrange equations.

Differential equations, Partial.

Equations of motion.

Vishik, M. I.

Physical Description:

ix, 136 pages : illustrations ; 25 cm.

Place of Publication:

Princeton : Princeton University Press, 2024.

Summary:

"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." - Supplied by publisher.

Contents:

General strategy: Background field and self-similar coordinates

Linear theory: Part I

Linear theory: Part II

Nonlinear theory.

Notes:

Includes bibliographical references (pages [131]-134) and index.

ISBN:

9780691257525

0691257523

9780691257532

0691257531

OCLC:

1377478655