Partial Regularity of Suitable Weak Solutions of the Navier--Stokes--Planck--Nernst--Poisson Equation

On the Interior Regularity of Suitable Weak Solutions to the Navier–Stokes Equations

Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled L p,q x,t -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the L p,q x,t -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the L p,q x,t -norm of the gradient of the vorticity with 3/p + 2/q ≤ ...

Regularity for Suitable Weak Solutions to the Navier-Stokes Equations in Critical Morrey Spaces

A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are invariant with respect to the Navier-Stokes equations scaling. The famous Caffarelli-Kohn-Nirenberg condition is contained in that class as a particular case. 1991...

Convergent Finite Element Discretizations of the Navier-stokes-nernst-planck-poisson System

We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin’s projection method to obtain an efficient approximation that converges to strong solutions at optimal rates. Mathematics Subject Classi...

Partial Regularity of Weak Solutions of the Viscoelastic Navier-Stokes Equations with Damping

We prove an analogue of the Caffarelli–Kohn–Nirenberg theorem for weak solutions of a system of PDEs that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of establishing the global-in-time existence of weak solutions of the well-known Oldroyd system.