On the free boundary problem for the Oldroyd-B Model in the maximal LpLp–LqLq regularity class

In the present work, we prove the local well-posedness of non-Newtonian compressible viscous barotropic fluid flow of Oldroyd-B type with free surface in a bounded domain of NN-dimensional Euclidean space (N≥2N≥2). The key step is to prove the maximal LpLp–LqLq regularity theorem for the linearized equation with the help of the RR-bounded solution operators for the corresponding resolvent problem and Weis’s operator valued Fourier multiplier theorem.