On Liouville-type theorems for the 2D stationary MHD equations

Liouville theorems on some indefinite equations

In this note, we present some Liouville type theorems about the nonnegative solutions to some indefinite elliptic equations.

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 ...

Liouville Theorem for 2d Navier-stokes Equations

(One may modify the question by putting various other restrictions on (L); for example, one can consider only steady-state solutions, or solutions with finite rate of dissipation or belonging to various other function spaces, etc.) We have proved a positive result for dimension n = 2 which we will discuss below, but let us begin by mentioning why the basic problem is interesting. Generally spea...

Some Remarks on Liouville Type Theorems

The goal of this note is to present elementary proofs of statements related to the Liouville theorem.

A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system