On the regularity of two-dimensional unsteady flows of heat-conducting generalized Newtonian fluids

Abstract

We study regularity properties of unsteady flows of an incompressible heat-conducting fluid in a two-dimensional spatially periodic setting. Under certain structural assumptions on the Cauchy stress that include generalizations of the Ladyzhenskaya or power-law like models we establish the existence of a classical solution to such problems.

Keywords

• Regularity
• Heat-conducting fluid
• Power-law like fluid
• Generalized Navier-Stokes-Fourier fluid
• Ladyzhenskaya system