Isett, Philip. <br/><br/>
Holder continuous Euler flows in three dimensions with compact support in time / 
Philip Isett. 
 -  Princeton University Press,  2017. 
 - 1 online resource 
 - Annals of Mathematics Studies ;  number 196 .
 - Annals of mathematics studies ;  no. 196. .
<br/><br/> Frontmatter --  Contents --  Preface --  Part I. Introduction --  Part II. General Considerations of the Scheme --  Part III. Basic Construction of the Correction --  Part IV. Obtaining Solutions from the Construction --  Part V. Construction of Regular Weak Solutions: Preliminaries --  Part VI Construction of Regular Weak Solutions: Estimating the Correction --  Part VII. Construction of Regular Weak Solutions: Estimating the New Stress --  Acknowledgments --  Appendices --  References --  Index 
<br/><br/> 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-H�older. In this book, Philip Isett 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 hidden symmetries--mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"--Used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem--has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture. 
<br/><br/><br/>In English. 
<br/><br/><label>ISBN: </label>1400885426 9781400885428 
<br/><br/><label>Standard No.: </label>10.1515/9781400885428  doi 
<br/><br/><label>Source: </label>985558  MIL 22573/ctt1h180j7  JSTOR 9452463  IEEE 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Fluid dynamics--Mathematics.<br/>Dynamique des fluides--Math�ematiques.<br/>TECHNOLOGY & ENGINEERING--Hydraulics.<br/>Fluid dynamics--Mathematics.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA911  / .I84 2017eb 
<br/><br/><label>Dewey Class. No.: </label>532.1