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Precise regularity results for the Euler equations. (English) Zbl 1048.35079
Using the methods of paradifferential calculus and regularity estimates in Besov (or Triebel-Lizorkin) spaces, the author proves the following condition for blow-up: if the maximal time \(T\) of existence of solution in smooth bounded domains is finite, then the \(L_\infty\) norm of velocity curl necessarily blows up on the time interval \([0;T]\).

MSC:
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35B40 Asymptotic behavior of solutions to PDEs
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