The third order Benjamin–Ono equation on the torus: Well-posedness, traveling waves and stability
Louise Gassot
Département de Mathématiques et Applications, École Normale Supérieure, CNRS, PSL University, 75005 Paris, France; Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d'Orsay, 91405 Orsay, France
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Abstract
We consider the third order Benjamin–Ono equation on the torus
We prove that for any , the flow map continuously extends to if , but does not admit a continuous extension to if . Moreover, we show that the extension is weakly sequentially continuous in if , but is not weakly sequentially continuous in . We then classify the traveling wave solutions for the third order Benjamin-Ono equation in and study their orbital stability.
Cite this article
Louise Gassot, The third order Benjamin–Ono equation on the torus: Well-posedness, traveling waves and stability. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 815–840
DOI 10.1016/J.ANIHPC.2020.09.004