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A Liouville theorem for the Euler equations in the plane

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Academic year: 2021

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Figure

Figure 1: The streamlines Γ x N and Γ y , the domain Ω, and the trajectory Σ
Figure 2: Non-intersecting arcs ξ([a, b]) with ξ([a, b]) ∩ (ξ(a), ξ(b)) = ∅ (top) and ξ([a, b]) ∩ L ξ(a),ξ(b) \[ξ(a), ξ(b)]
Figure 3: Middle, left, right, double and exterior arcs, relatively to the segment [ξ(a), ξ(b)]
Figure 4: The arcs ξ([τ i , τ i 0 ]) and ξ([τ i+1 , τ i+1 0 ]) are left arcs, the arc ξ([τ i , τ i+1 0 ]) is non- non-intersecting
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