{"product_id":"instability-and-non-uniqueness-for-the-2d-euler-equations-after-m-vishik-9780691257532","title":"Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik: (Ams-219)","description":"\u003cp\u003e\u003cb\u003eAn essential companion to M. Vishik's groundbreaking work in fluid mechanics\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThe 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 \u003ci\u003eL\u003c\/i\u003e\u003ci\u003e p\u003c\/i\u003e setting.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eDallas Albritton\u003c\/b\u003e is a mathematician and NSF postdoctoral fellow at Princeton University. \u003cb\u003eElia Brué\u003c\/b\u003e is a mathematician at Bocconi University in Milan. \u003cb\u003eMaria Colombo\u003c\/b\u003e is a mathematician and professor at the Swiss Federal Institute of Technology in Lausanne. \u003cb\u003eCamillo De Lellis\u003c\/b\u003e is a mathematician at the Institute for Advanced Study in Princeton. \u003cb\u003eVikram Giri\u003c\/b\u003e is a mathematician at Princeton. \u003cb\u003eMaximilian Janisch\u003c\/b\u003e is a PhD student in mathematics at the University of Zurich. \u003cb\u003eHyunju Kwon\u003c\/b\u003e is a Hermann Weyl Instructor at ETH Zurich.\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":50394706018578,"sku":"9780691257532","price":78.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_b10630a0-ef9b-401d-a45f-e1b8ba7b2982.jpg?v=1729014378","url":"https:\/\/surprise-castle.myshopify.com\/products\/instability-and-non-uniqueness-for-the-2d-euler-equations-after-m-vishik-9780691257532","provider":"Surprise Castle","version":"1.0","type":"link"}