Local Existence of Strong Solutions of a Fluid–Structure Interaction Model

Please always quote using this URN: urn:nbn:de:bvb:20-opus-235097
  • We are interested in studying a system coupling the compressible Navier–Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler–Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.

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Author: Sourav MitraORCiD
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):Journal of Mathematical Fluid Mechanics
Year of Completion:2020
Article Number:60
Source:Journal of Mathematical Fluid Mechanics 22, 60 (2020). https://doi.org/10.1007/s00021-020-00520-8
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:Euler–Bernoulli damped beam; compressible fluid; fluid–structure interaction model; local existence
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Dxx Generalized solutions / 35D35 Strong solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R37 Moving boundary problems
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Dxx Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) / 74D99 None of the above, but in this section
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Nxx Compressible fluids and gas dynamics, general / 76N10 Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C20 Systems governed by partial differential equations
Release Date:2021/06/11
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International