Estimates of Mild Solutions of Navier–Stokes Equations in Weak Herz-Type Besov–Morrey Spaces

Estimates of suitable weak solutions to the Navier-Stokes equations in critical Morrey spaces

We prove some estimates for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations under assumptions that certain invariant functionals of the velocity field are bounded. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

CBMO Estimates for Multilinear Commutator of Marcinkiewicz Operator in Herz and Morrey-Herz Spaces

In this paper, we establish CBMO estimates for the multilinear commutator related to the Marcinkiewicz operator in Herz and Morrey-Herz spaces.

Gradient Estimates for Weak Solutions of A-Harmonic Equations

Weak Solutions for Dislocation Type Equations

We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author in [9, 7]. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak soluti...