Local well-posedness of incompressible viscous fluids in bounded cylinders with 90^∘-contact angle

2020/08/13 by Keiichi Watanabe, Watanabe, Keiichi
Computer Science · Mathematics · #76D45 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Primary: 35R35 #Secondary: 76D03

paper · pdf · doi:10.48550/arxiv.2008.05617

openalex publication_date 2020/08/13 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

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. In contrast to the strategy in Wilke (2013), we study the transformed problem in an L^p-in-time and L^q-in-space setting, which yields the optimal regularity of the initial data.

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