Global existence and uniqueness for the Lake equations with vanishing topography : elliptic estimates for degenerate equations

Didier Bresch (1) , Guy Metivier (2)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 IMB - Institut de Mathématiques de Bordeaux

This paper deals with global existence and uniqueness for the lake equations with a bottom topography vanishing on the shore. Our result generalizes previous studies that assumed the depth to be nondegenerate. Elliptic estimates for degenerate equations has to be established studying the behavior of the associated Green function.

Mots clés: weighted Sobolev spaces; degenerate elliptic equation; Regularity result; Youdovitch's method; vorticity-Stream function formulation; Youdovitch's method.

Domaines: Equations aux dérivées partielles [math.AP]

Didier Bresch, Guy Metivier. Global existence and uniqueness for the Lake equations with vanishing topography : elliptic estimates for degenerate equations. Nonlinearity, 2006, 19 (3), pp.591-610. ⟨10.1088/0951-7715/19/3/004⟩. ⟨hal-00113732⟩