6 papers
Global well-posedness and long-time asymptotics of a general nonlinear non-local Burgers Equation
Jin Tan, Francois Vigneron
This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads ,…
Variation on a theme by Kiselev and Nazarov: H{ö}lder estimates for non-local transport-diffusion, along a non-divergence-free BMO field
Ioann Vasilyev, François Vigneron
We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator,and a general advection field in BMO, as long as the order of t…
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…
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 with , and ~: \[\inf_{\substack{u\in H^1_0(Ω) \|u\|_{L^q}=1}}\int_Ωa(x,u)|\nab…
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 …
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 with ~: We show that minimizers…