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UID:20260414T231115EDT-1956IHIiE6@132.216.98.100
DTSTAMP:20260415T031115Z
DESCRIPTION:~~In this talk we shall discuss some linkages between the PDEs 
 of fluid dynamics and the Gauss-Codazzi-Ricci equations for isometric embe
 ddings of Riemannian manifolds. First\, we prove the existence of isometri
 c embeddings of certain negatively curved 2-dimensional surfaces into $\ma
 thbb{R}^3$ via a ''fluid dynamic formulation'' of the Gauss-Codazzi equati
 ons. The key technique is the method of compensated compactness\, previous
 ly used by Lax\, DiPerna\, Morawetz and others to show the existence of so
 lutions to hyperbolic conservation laws and transonic gas dynamics. Second
 \, we give global and intrinsic proofs for the weak rigidity of isometric 
 embeddings of Riemannian/semi-Riemannian manifolds\, using the generalised
  compensated compactness theorems recently established in the geometric se
 ttings. Third\, we discuss an elementary proof for the existence of infini
 tely many ''wild'' solutions to the Euler equations\, previously construct
 ed by De Lellis\, Szekelyhidi and others via convex integrations. Our proo
 f relies on a direct dynamic analogue with the isometric embeddings and th
 e celebrated results by Nash and Gromov. The talk is based on joint works 
 with G.-Q. Chen (Oxford)\, M. Slemrod (Wisconsin-Madison)\, Dehua Wang (Pi
 ttsburgh)\, and Amit Acharya (Carnegie Mellon).\n\n \n
DTSTART:20170612T173000Z
DTEND:20170612T183000Z
LOCATION:room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Siran Li (Oxford\, CRM\, McGill)
URL:https://www.mcgill.ca/mathstat/channels/event/siran-li-oxford-crm-mcgil
 l-268492
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