Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities
For an evolutionary nonlinear fluid model characterized by the viscosity being a decreasing function of the modulus of the symmetric velocity gradient we establish global-in-time existence of the solution with Hölder continuous velocity gradients. Such a solution is unique in the class of weak solutions. We deal with the two dimensional space periodic problem.
scientific article; zbMATH DE number 1761064