Liouville theorem for Beltrami flow

Nikolai Nadirashvili (1)

1 I2M - Institut de Mathématiques de Marseille

The author proves that if v∈C1(ℝ3) is a Beltrami solution of the stationary Euler equations v∇v+∇p=0,∇⋅v=0, and v∈Lp(ℝ3) or v(x)=o(1|x|) as x→∞, then v≡0.

Mots clés: Beltrami flow; Liouville theorem; tensor equations; Euler equation

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Nikolai Nadirashvili. Liouville theorem for Beltrami flow. Geometric And Functional Analysis, 2014, 24 (3), pp.916--921. ⟨10.1007/s00039-014-0281-8⟩. ⟨hal-01335877⟩