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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik (AMS-219) (Annals of Mathematics Studies, 219) free ebook download

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Author(s):	Camillo De Lellis, Elia Brue

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	0691257531
Pages:	148	OCR:		Quality:		ISBN13:
Uploader:	rubybook	Upload Date:	2/5/2024 9:27:45 PM

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0691257531 pdf
An essential companion to M. Vishik's groundbreaking work in fluid mechanicsThe 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.

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Tags: AMS-219 Annals Equations Euler Instability Mathematics Non-uniqueness Studies Vishik

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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik (AMS-219) (Annals of Mathematics Studies, 219) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics