The cubic Szegő flow at low regularity
Patrick Gérard1 ; Herbert Koch2
1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris–Saclay 91405 Orsay France
2 Mathematisches Institut Universität Bonn D-53115 Bonn Germany
Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 14, 14 p.

We prove that the cubic Szegő equation is well posed on the space BMO + of functions of bounded mean oscillation in the Hardy class of the disc, and we establish the Hölder regularity of this flow in the L 2 distance. We also show that the Cauchy problem is illposed on the corresponding L ∞ space.

Publié le :
DOI : 10.5802/slsedp.105
Patrick Gérard 1 ; Herbert Koch 2

1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris–Saclay 91405 Orsay France
2 Mathematisches Institut Universität Bonn D-53115 Bonn Germany 
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Patrick Gérard; Herbert Koch. The cubic Szegő flow at low regularity. Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 14, 14 p. doi : 10.5802/slsedp.105. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.105/

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