Axisymmetric Solutions to Coupled Navier-Stokes/Allen-Cahn Equations

A Regularity Criterion for the 3D Incompressible Density-Dependent Navier-Stokes-Allen-Cahn Equations

The Graduate School AN ENERGETIC VARIATIONAL APPROACH TO MATHEMATICAL MODELING OF CHARGED FLUIDS : CHARGE PHASES , SIMULATION AND WELL POSEDNESS

In thesis we propose a mathematical model of electrolyte fluid and interface systems. The model is based on a coupling between the Navier-Stokes equations of an incompressible fluid, the Nernst-Plank-Poisson equations of a diffuse, binary electrolyte, and the phase field Allen-Cahn equation. The coupling is derived in the energetic variational framework and guarantees the consistent exchange of...

On the regularity of the axisymmetric solutions of the Navier-Stokes equations

Weobtain improved regularity criteria for the axisymmetricweak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrability of single component of vorticity or velocity fields, in terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these criteria we derive new a prio...

A Regularity Criterion for the Angular Velocity Component in Axisymmetric Navier-stokes Equations

We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions

We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smo...