Geodesic Completeness for Sobolev $H^{s}$-metrics on the Diffeomorphisms Group of the Circle

Joachim Escher (1) , Boris Kolev (2)

1 IFAM - Institute for Applied Mathematics
2 I2M - Institut de Mathématiques de Marseille

We prove that the weak Riemannian metric induced by the fractional Sobolev norm $H^s$ on the diffeomorphisms group of the circle is geodesically complete, provided $s>3/2$.

Mots clés: diffeomorphism group; fractional Sobolev metrics; Euler equation

Domaines: Physique mathématique [math-ph]

Joachim Escher, Boris Kolev. Geodesic Completeness for Sobolev $H^{s}$-metrics on the Diffeomorphisms Group of the Circle. Journal of Evolution Equations, 2014, 14 (4-5), pp.949--968. ⟨10.1007/s00028-014-0245-3⟩. ⟨hal-00851606v2⟩