{"product_id":"hzilder-continuous-euler-flows-in-philip-isett-9780691174839","title":"Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time","description":"\u003cp\u003eMotivated 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. 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThe 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Philip Isett\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691174830\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691174839\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/21\/2017\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 216\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.65lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.20h x 5.90w x 0.40d","brand":"Philip Isett","offers":[{"title":"Paperback","offer_id":48448885981439,"sku":"9780691174839","price":93.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5dc403f7-d674-4bd1-82c2-abe57de935c6.jpg?v=1777261007","url":"https:\/\/www.whiterainbookhouse.com\/products\/hzilder-continuous-euler-flows-in-philip-isett-9780691174839","provider":"WR Book House","version":"1.0","type":"link"}