Publication at Faculty of Mathematics and Physics |
2011
Abstract
In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity increasing with a scalar quantity k that evolves according to an evolutionary convection diffusion equation with the right hand side that is merely L1-integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.