The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptoticâ€¦ (More)

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. Thisâ€¦ (More)

We construct self-similar solutions for three-dimensional incom-pressible Navier-Stokes equations, providing some examples of functional spaces where this can be done. We apply our results to aâ€¦ (More)

The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier-Stokes system. The Marcinkiewicz space L is used toâ€¦ (More)

We derive various estimates for strong solutions to the NavierStokes equations in C([0, T ), L3(R3 )) that allow us to prove some regularity results on the kinematic bilinear term. Introduction andâ€¦ (More)

The goal of this work is to present an approach to the homogeneous Boltz-mann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to theâ€¦ (More)

In this paper we study the blow-up criterion of smooth solution to the ideal MHD equations in Rn. By means of the Fourier frequency localization and Bony paraproduct decomposition, we show a losingâ€¦ (More)

In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model where the dislocationâ€¦ (More)

We consider the 2-dimensional quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we proveâ€¦ (More)