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Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Abstract

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with ... More

Keywords: weak solution, Lars Onsager, Euler equations, convex integration, fluid dynamics, transport equations, algebra, nonzero solution, Onsager's conjecture, Main Lemma

Bibliographic Information

Print publication date: 2017 Print ISBN-13: 9780691174822
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691174822.001.0001

Authors

Affiliations are at time of print publication.

Philip Isett, author
Massachusetts Institute of Technology

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