2025/07/31 by Eiter, Thomas, Silvestre, Ana Leonor
#35B10 #35Q30 #76D05 #76D07 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.23697
We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain Ω⊂ \mathbb R3 that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains Ω∩ BR, incorporating appropriate artificial boundary conditions on ∂ BR. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius R, showing that, as R → ∞, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow.