AXISYMMETRIC SOLUTIONS TO COUPLED NAVIER–STOKES/ALLEN–CAHN EQUATIONS

摘要

We investigate a family of axisymmetric solutions to a coupling of Navier–Stokes and Allen–Cahn equations in R~3. First, a one-dimensional system of equations is derived from the method of separation of variables, which approximates the three-dimensional system along its symmetry axis. Then based on them, by adding perturbation terms, we construct finite energy solutions to the threedimensional system. We prove the global regularity of the constructed solutions in both large viscosity and small initial data cases. These solutions can be considered as perturbations near infinite-energy solutions.