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. 815–840DOI 10.1016/J.ANIHPC.2020.09.004