Publication at Faculty of Mathematics and Physics |
2011
Abstract
We establish an L2-regularity result for a weak solution of the evolutionary Stokes–Fourier system. Although this system does not contain the convective terms, the fact that the viscosity depends on the temperature makes the considered system of partial differential equations nonlinear.
The result holds for a class of the viscosities that includes the Arrhenius formula as a special case. For simplicity, we restrict ourselves to a spatially periodic setting in this study.