A variational approach to hyperbolic evolutions and fluid-structure interactions

  • Barbora Benešová

    Charles University, Praha, Czechia
  • Malte Kampschulte

    Charles University, Praha, Czechia
  • Sebastian Schwarzacher

    Charles University, Praha, Czechia; Uppsala University, Sweden
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Abstract

We show the existence of a weak solution for a system of partial differential equations describing the motion of a flexible solid inside a fluid: A nonlinear, viscoelastic, -dimensional bulk solid governed by a PDE including inertia is interacting with an incompressible fluid governed by the (-dimensional) Navier–Stokes equation for . The result is the first allowing for large bulk deformations in the regime of long time existence for fluid-structure interactions. The existence is achieved by introducing a novel variational scheme involving two time-scales that allows us to extend the method of minimizing movements to hyperbolic problems involving nonconvex and degenerate energies.

Cite this article

Barbora Benešová, Malte Kampschulte, Sebastian Schwarzacher, A variational approach to hyperbolic evolutions and fluid-structure interactions. J. Eur. Math. Soc. 26 (2024), no. 12, pp. 4615–4697

DOI 10.4171/JEMS/1353