2 citations · 2 across the 1 of their papers we have counts for
6 papers
On the regularity of temperature fronts for the 3D viscous Boussinesq system
Omar Lazar, Yatao Li, Liutang Xue
We study the temperature front problem for the 3D viscous Boussinesq equation. We prove that the (, ) and regularity of a temperature fron…
Paralinearization of the Muskat equation and application to the Cauchy problem
Thomas Alazard, Omar Lazar
We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-pose…
Growth in the Muskat problem
Rafael Granero-Belinchón, Omar Lazar
We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initia…
On the local and global existence of solutions to 1D transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &θ_t+uθ_x+νΛ^γθ=0, \\ & u=\mathcal{N}(θ), \end{split} \end{equat…
Global well-posedness for the 2D stable Muskat problem in
Diego Cordoba, Omar Lazar
We prove a global existence result of a unique strong solution in with small semi-norm for the 2D Muskat problem, hence allowing the…
Regularity results for a class of generalized surface quasi-geostrophic equations
Omar Lazar, Liutang Xue
We show a global existence result of weak solutions for a class of generalized Surface Quasi-Geostrophic equation in the inviscid case. We also prove the global regularity of such…