Local well-posedness of incompressible viscous fluids in bounded cylinders with 90°-contact angle. (June 2022)

• Record Type: Journal Article
• Authors: Watanabe, Keiichi
• Is Part Of: Nonlinear analysis. Volume 65(2022)
• Publication Date: 2022-06
• Subjects: Moving contact lines -- Free boundary problems -- Navier–Stokes equations -- Maximal regularity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103489
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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 .