Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation

In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model satisfy the local energy inequality. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions trough a Fourier-Galerkin finite-dimensional approximation in the space variables

Global regularity for systems with pp-structure depending on the symmetric gradient

In this paper we study on smooth bounded domains the global regularity (up to the boundary) for weak solutions to systems having $p$-structure depending only on the symmetric part of the gradient.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1607.0629

A note on regularity of weak solutions of the Navier-Stokes equations in R^n

In this paper we consider the n dimensional Navier-Stokes equations and we prove a new regularity criterion for weak solutions. More precisely, if n = 3,4 we show that the “smallness” of at least n-1 components of the velocity in L^infty(0,T;L_w(R^n)) is sufficient to ensure regularity of the weak solutions

An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case

We study with elementary tools the stationary 3D Navier-Stokes equations in a flat domain, equipped with Navier (slip without friction) boundary conditions. We prove existence and uniqueness of weak, strong, and very weak solutions in appropriate Banach spaces and most of the result hold true without restrictions on the size of the data. Results are partially known, but our approach allows us to give rather elementary and self-contained proofs

Some results on the two-dimensional dissipative Euler equations

We make a review of some recent results concerning special solutions and behavior at infinity for 2D dissipative Euler equations. In particular, we give a simplified proof --in the space-periodic setting-- of the uniform space/time boundedness of the first derivatives of the velocity, under suitable assumptions on the external force and on the dissipation (damping) coefficient. This is used to sketch the proof of existence of almost-periodic solutions