Work

Inviscid fluid interacting with a nonlinear two-dimensional plate

Year: 2024

Type: article

Abstract: We address a moving boundary problem that consists of a system of equations modeling an inviscid fluid interacting with a two-dimensional nonlinear Koiter plate at the boundary. We derive a priori estimates needed to prove the local-in-time existence of solutions. We use the Arbitrary Lagrange Euler (ALE) coordinates to fix the domain and obtain careful estimates for the nonlinear Koiter plate, ALE velocity, and pressure without any viscoelastic smoothing. For the nonlinear Koiter plate, higher order energy estimates are obtained, whereas estimates for the ALE pressure are obtained by setting up an elliptic problem. For the ALE velocity, the bounds are obtained through div-curl estimates by estimating the ALE vorticity. We then extend our results in two directions: (1) to include fractional Sobolev spaces and (2) to incorporate the normalized second fundamental form.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/534

Authors: Abhishek Balakrishna, Igor Kukavica, Boris Muha, Amjad Tuffaha

Institutions: University of Southern California, University of Zagreb, American University of Sharjah

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Hrvatska Zaklada za Znanost

Awards: Regularity and Asymptotic Behavior in Fluid Dynamics, Mathematical theory of next generation fluid-structure interactions models