Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation

Luis Gustavo Farah (1) , Frédéric Rousset (2) , Nikolay Tzvetkov (3)

1 DM - UFMG - Departamento de Matemática [Minas Gerais]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We prove a multidimensional oscillatory integral estimate using a variant ofthestationaryphasemethod. Asaconsequence, weobtainglobalwell-posednessfor small data for the 2D Boussinesq equation u (tt) + (u (xx) + u (2) - u) (xx) - u (yy) = 0.

Mots clés: multidimensional oscillatory integral; 2D Boussinesq equation; global well-posedness

Domaines: Equations aux dérivées partielles [math.AP]

Luis Gustavo Farah, Frédéric Rousset, Nikolay Tzvetkov. Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, 2012, 43 (4), pp.655-679. ⟨10.1007/s00574-012-0031-1⟩. ⟨hal-00784793⟩