F. Vigneron

activity

20112019

collaborators

4 papers

math-ph2019

On the Wiener-Khinchin transform of functions that behave as approximate power-laws. Applications to fluid turbulence

Francois Vigneron

As we all know, the Fourier transform is continuous in the weak sense of tempered distribution; this ensures the weak stability of Fourier pairs. This article investigates a strong…

math.AP2017

Existence of Solutions of a Non-Linear Eigenvalue Problem with a Variable Weight

Rejeb Hadiji, Francois Vigneron

We study the non-linear minimization problem on $H_{0}^{1} (Ω) \subset L^{q}$ with $q = \frac{2 n}{n - 2}$ , $α > 0$ and $n \geq 4$ ~: \[\inf_{\substack{u\in H^1_0(Ω) \|u\|_{L^q}=1}}\int_Ωa(x,u)|\nab…

math.AP2015

Global Well-Posedness Of A Non-Local Burgers Equation: The Periodic Case

Cyril Imbert, Roman Shvydkoy, Francois Vigneron

This paper is concerned with the study of a non-local Burgers equation for positive bounded periodic initial data. The equation reads $u_{t} - u ∣\nabla∣ u + ∣\nabla∣ (u^{2}) = 0.$ …

math.AP2011

Non-Linear Effects in a Yamabe-Type Problem with Quasi-Linear Weight

Soohyun Bae, Rejeb Hadiji, Francois Vigneron +1

We study the quasi-linear minimization problem on $H_{0}^{1} (Ω) \subset L^{q}$ with $q = \frac{2 n}{n - 2}$ ~: $∥ u ∥_{L^{q}} = 1 in f \int_{Ω} (1 + ∣ x ∣^{β} ∣ u ∣^{k}) ∣\nabla u ∣^{2} .$ We show that minimizers…