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We show that solutions u(x, t) of the non-stationnary incompressible Navier–Stokes system in R d (d ≥ 2) starting from mild decaying data a behave as |x| → ∞ as a potential field: u(x, t) = e t∆ a(x) + γ d ∇ x h,k δ h,k |x| 2 − dx h x k d|x| d+2 K h,k (t) + o 1 |x| d+1 (i) where γ d is a constant and K h,k = t 0 (u h |u k) L 2 is the energy matrix… (More)
AIMS In heart failure (HF), mitochondrial quality control and autophagy are progressively impaired, but the role of oxidative stress in this process and its underlying mechanism remain to be defined. By degrading norepinephrine and serotonin, the mitochondrial enzyme, monoamine oxidase-A (MAO-A), is a potent source of reactive oxygen species (ROS) in the… (More)
We study the behavior at innity, with respect to the space variable, of solutions to the magnetohydrodynamics equations in R d. We prove that if the initial magnetic eld decays suciently fast, then the plasma ow behaves as a solution of the free nonstationnary NavierStokes equations when |x| → +∞, and that the magnetic eld will govern the decay of the… (More)
We study the non-linear minimization problem on H 1 0 (Ω) ⊂ L q with q = 2n n−2 : inf u L q =1 Ω (1 + |x| β |u| k)|∇u| 2. We show that minimizers exist only in the range β < kn/q which corresponds to a dominant non-linear term. On the contrary, the linear influence for β ≥ kn/q prevents their existence.