Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.

Browsing by Subject "stokes flow"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow
    (2018-05) Rodenberg, Analise
    In the work that follows we investigate a class of problems where a one dimensional closed elastic structure is immersed in a plane of steady Stokes flow. The dynamics are governed by a boundary integral equation describing the configuration of the immersed structure. Depending on the choice of elasticity law, we break our class into either a semilinear or fully nonlinear system of equations. In the nonlinear setting, we prove that the linearization of the system generates an analytic semigroup and use it to prove local existence and uniqueness in low regularity H\"{o}lder spaces. In the semilinear setting, we remove the principle operator via small scale decomposition and use it to build similar local existence results. Further, we establish spatial smoothness of solutions by careful estimates on a class of commutators. Using these regularity results, we are able to establish that the only equilibria of the system are uniformly parameterized circles which we then prove nonlinear stability about. Finally, we identify a quantity which classifies global-in-time behavior.