Geodesic
Inviscid fluid interacting with a nonlinear two-dimensional plate
Abhishek Balakrishna1 orcid ; Igor Kukavica1 orcid ; Boris Muha2 orcid ; Amjad Tuffaha3 orcid
1University of Southern California, Los Angeles, USA
2University of Zagreb, Zagreb, Croatia
3American University of Sharjah, Sharjah, United Arab Emirates
Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 141-175

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DOI

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.
DOI : 10.4171/ifb/534
Classification : 35Q31, 35Q35, 35R37, 74B20, 74K20
Mots-clés : fluid structure interaction, fluid plate interaction, inviscid fluid, nonlinear plate, von Karman nonlinearity, Euler equations

Abhishek Balakrishna  1   ; Igor Kukavica  1   ; Boris Muha  2   ; Amjad Tuffaha  3

1 University of Southern California, Los Angeles, USA
2 University of Zagreb, Zagreb, Croatia
3 American University of Sharjah, Sharjah, United Arab Emirates 
Abhishek Balakrishna; Igor Kukavica; Boris Muha; Amjad Tuffaha. Inviscid fluid interacting with a nonlinear two-dimensional plate. Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 141-175. doi: 10.4171/ifb/534
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     title = {Inviscid fluid interacting with a nonlinear two-dimensional plate},
     journal = {Interfaces and free boundaries},
     pages = {141--175},
     year = {2025},
     volume = {27},
     number = {1},
     doi = {10.4171/ifb/534},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/534/}
}
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