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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik

Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik

Brué, Elia
Lellis, Camillo De
Albritton, Dallas

Hardcover

Series: Annals of Mathematics Studies, Book 215

General MathematicsPhysics

ISBN10: 0691257523
ISBN13: 9780691257525
Publisher: Princeton University Press
Published: Feb 13 2024
Pages: 144
Weight: 0.85
Height: 0.59 Width: 6.14 Depth: 9.21
Language: English

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.

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