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\(C^ \infty\)-solutions in time, \(n\)- \(\log\) Lipschitz bounded in space and Euler equation. (Solutions \(C^ \infty\) en temps, \(n\)-\(\log\) Lipschitz bornées en espace et équation d’Euler.) (French) Zbl 0835.76012
Summary: On all \([0,T]\), we solve the two-dimensional incompressible Euler equations in \(L^\infty\) within Lipschitz frame \([u, \text{rot} (u)\) are bounded without integrability conditions], and we show that the \(n\)- th derivative of the solution has the estimate \(C |x |\log |x |^n\) for module of continuity; each derivation in \(t\) is then followed by a loss of regularity in \(x\).

MSC:
76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
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