Uniqueness and regularity of flows of generalized Newtonian fluids
Petr Kaplicky
Charles University Czech Rep
Co-Author(s): M. Bul\`\i\v cek, F. Ettwein, D. Pra\v z\`ak
Abstract:
We study regularity and uniqueness of flows of generalized Newtonian fluids. The prototypical example of the Cauchy stress tensor has the form $\mathbb T(\mathbb D)=(1+|\mathbb D|^2)^{(p-2)/2}\mathbb D$ for some growth parameter $p>1$. For $p\geq 11/5$ we show sufficient regularity of any solution to obtain its uniqueness. We remark that the bound $p\geq 11/5$ corresponds to the situation when we can test the weak formulation of the equation with the solution under its natural regularity.