ﻻ يوجد ملخص باللغة العربية
We study the Cauchy problem for the quasi-geostrophic equations in a unit ball of the two dimensional space with the homogeneous Dirichlet boundary condition. We show the existence, the uniqueness of the strong solution in the framework of Besov spaces. We establish a spectral localization technique and commutator estimates.
This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the advected scalar b
In this paper, we present an extension of Uzawas algorithm and apply it to build approximating sequences of mean field games systems. We prove that Uzawas iterations can be used in a more general situation than the one in it is usually used. We then
In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new families of global classical solutions for to the generalized surface quas
We construct examples of solutions to the conservative surface quasi-geostrophic (SQG) equation that must either exhibit infinite in time growth of derivatives or blow up in finite time.
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homog