Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction

DOI10.1090/tran/8423zbMath1469.35176arXiv2104.03434OpenAlexW3159862780MaRDI QIDQ5004557

Sunčica Čanić, Jeffrey Kuan

Publication date: 2 August 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.03434

zbMATH Keywords

viscous nonlinear wave equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear elasticity (74B20) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Ill-posed problems for PDEs (35R25) Second-order nonlinear hyperbolic equations (35L70) PDEs with randomness, stochastic partial differential equations (35R60) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) PDEs in connection with mechanics of deformable solids (35Q74) Initial value problems for PDEs of mixed type (35M11)

Related Items

Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction ⋮ Well-posedness of solutions to stochastic fluid-structure interaction ⋮ A stochastically perturbed fluid-structure interaction problem modeled by a stochastic viscous wave equation ⋮ On the two-dimensional singular stochastic viscous nonlinear wave equations

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