41 citations · 85 across the 9 of their papers we have counts for
13 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…
On the dynamics of the roots of polynomials under differentiation
Thomas Alazard, Omar Lazar, Quoc-Hung Nguyen
This article is devoted to the study of a nonlinear and nonlocal parabolic equation introduced by Stefan Steinerberger to study the roots of polynomials under differentiation; it a…
Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space
Francisco Gancedo, Omar Lazar
We prove that the 3D stable Muskat problem is globally well-posed in the critical Sobolev space provided that the semi-norm $\Vert f_0 \Vert_{\dot…
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…
Global existence of weak solutions to dissipative transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider 1D dissipative transport equations with nonlocal velocity field: \[ θ_t+uθ_x+δu_{x} θ+Λ^γθ=0, \quad u=\mathcal{N}(θ), \] where is a nonlocal operator give…
On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion
Omar Lazar
We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space …
Infinite energy solutions for a 1D transport equation with nonlocal velocity
Omar Lazar, Pierre-Gilles Lemarié-Rieusset
We study a one dimensional dissipative transport equation with nonlocal velocity and critical dissipation. We consider the Cauchy problem for initial values with infinite energy. T…
Global and local existence for the dissipative critical SQG equation with small oscillations
Omar Lazar
This article is devoted to the study of the critical dissipative surface quasi-geostrophic equation in . For any initial data belonging to the space $…
Global existence for the critical dissipative surface quasi-geostrophic equation
Omar Lazar
In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in . Motivated by the study of the homogeneous statistical solutions of t…