Large Time Decay of the Oseen Flow in Exterior Domains Subject to the Navier Slip-with-Friction Boundary Condition
Year: 2026
Type: article
Abstract: Consider the motion of a viscous incompressible fluid filling a 3D exterior domain $$\Omega $$ Ω subject to the Navier slip-with-friction boundary condition as well as outflow at infinity. For the Oseen system as the linearization, we discuss the resolvent set under a certain relationship among the geometry of the boundary $$\partial \Omega $$ ∂ Ω , friction coefficient $$\alpha (x)$$ α ( x ) and the outflow $$u_\infty $$ u ∞ . We then study the regularity of the resolvent near the origin in the complex plane to develop $$L^q$$ L q - $$L^r$$ L r decay estimates of the Oseen semigroup provided that $$\alpha (x)+u_\infty \cdot \nu (x)/2\ge 0$$ α ( x ) + u ∞ · ν ( x ) / 2 ≥ 0 for every $$x\in \partial \Omega $$ x ∈ ∂ Ω , where $$\nu (x)$$ ν ( x ) stands for the outward unit normal to the boundary $$\partial \Omega $$ ∂ Ω .
Author: Toshiaki Hishida
Institution: Nagoya University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
Award: 粘性流と剛体運動の相互作用の数学的理論の新展開
OpenAlex ID: W7171032503