Local well-posedness of incompressible viscous fluids in bounded cylinders with 90°-contact angle.

We consider a free boundary problem of the Navier–Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90 ∘ -contact angle condition is posed. We show that for given T > 0 the problem is local well-posed on (0 , T) provided that the initial data are small. We study the transformed problem in an L p -in-time and L q -in-space setting with 2 < p < ∞ and 3 < q < ∞ satisfying 2 / p + 3 / q < 1 , which provides a weaker setting than the one that was allowed by Wilke (2020) whose case was p = q > 5. [ABSTRACT FROM AUTHOR]