2 8 Fe b 20 09 On the Liouville theorem for the Navier - Stokes and the Euler equations
نویسنده
چکیده
In this paper we prove that any weak solution v to the incom-pressible Navier-Stokes/Euler equations in N 2 (s − 2). Similar result also holds for the viscous/inviscid MHD equations in R N with N ≥ 3.
منابع مشابه
Liouville type of theorems with weights for the Navier-Stokes equations and the Euler equations
We study Liouville type of theorems for the Navier-Stokes and the Euler equations on R N , N ≥ 2. Specifically, we prove that if a weak solution (v, p) satisfies |v| 2 +|p| ∈ L 1 (0, T ; L 1 (R N , w 1 (x)dx)) and R N p(x, t)w 2 (x)dx ≥ 0 for some weight functions w 1 (x) and w 2 (x), then the solution is trivial, namely v = 0 almost everywhere on R N × (0, T). Similar results hold for the MHD ...
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تاریخ انتشار 2009