LpLp-theory for a generalized nonlinear viscoelastic fluid model of differential type in various domains

This paper studies a coupled system of hyperbolic and parabolic equations governing the motion of viscoelastic, incompressible fluids on various domains. The model under consideration covers a wide range of nonlinear fluids including generalized Newtonian fluids, generalized Oldroyd-B fluids or Peterlin approximations. Existence and uniqueness of strong LpLp-solutions for large times are proved for small data, for arbitrarily large data local well-posedness is shown.