On the wellposedness of the KdV/KdV2 equations and their frequency maps

Kappeler, Thomas; Molnar, Jan-Cornelius

doi:10.1016/j.anihpc.2017.03.003

Kappeler, Thomas ; Molnar, Jan-Cornelius

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 101-160.

Résumé

In form of a case study for the KdV and the KdV2 equations, we present a novel approach of representing the frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include convexity properties of the Hamiltonians and wellposedness results in spaces of low regularity. In particular, it is proved that on $H^{s}$ the KdV2 equation is $C^{0}$ -wellposed if $s ⩾ 0$ and illposed (in a strong sense) if $s < 0$ .

MR Zbl

DOI : 10.1016/j.anihpc.2017.03.003

Classification : 37K10, 35Q53, 35D05
Mots clés : KdV equation, KdV2 equation, Frequency map, Well-posedness, Ill-posedness, Convexity properties of Hamiltonians of integrable PDEs

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     title = {On the wellposedness of the {KdV/KdV2} equations and their frequency maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {101--160},
     publisher = {Elsevier},
     volume = {35},
     number = {1},
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}

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Kappeler, Thomas; Molnar, Jan-Cornelius. On the wellposedness of the KdV/KdV2 equations and their frequency maps. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 101-160. doi : 10.1016/j.anihpc.2017.03.003. http://www.numdam.org/articles/10.1016/j.anihpc.2017.03.003/

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