Global Well-Posedness of Incompressible Elastodynamics in Three-Dimensional Thin Domain

DOI10.1137/20M1383872zbMath1483.35249arXiv2104.09077OpenAlexW3215112937MaRDI QIDQ5014294

Fan Wang, Yuan Cai

Publication date: 1 December 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.09077

zbMATH Keywords

thin domainglobal well-posednessincompressible elastodynamics

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Thin bodies, structures (74K99) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with mechanics of deformable solids (35Q74) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Classical solutions to PDEs (35A09)

Cites Work

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• Global solutions to repulsive Hookean elastodynamics
• Global existence for the 2D incompressible isotropic elastodynamics for small initial data
• Global existence for the multi-dimensional compressible viscoelastic flows
• On 2D viscoelasticity with small strain
• Global well-posedness for compressible viscoelastic fluids near equilibrium
• Regularity of the Navier-Stokes equation in a thin periodic domain with large data
• On the regularity of the Navier-Stokes equation in a thin periodic domain
• Global solutions for incompressible viscoelastic fluids
• Global existence for systems of nonlinear wave equations in two space dimensions
• Lectures on nonlinear hyperbolic differential equations
• Nonresonance and global existence of prestressed nonlinear elastic waves
• Global existence of nonlinear elastic waves
• Reaction-diffusion equation on thin domains
• The null condition and global existence of nonlinear elastic waves
• Global existence for systems of nonlinear wave equations in two space dimensions. II
• Global regularity of the Navier-Stokes equations on 3D periodic thin domain with large data
• Uniform bound of the highest energy for the three dimensional incompressible elastodynamics
• Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions
• Global existence for a 2D incompressible viscoelastic model with small strain
• Global Well-Posedness of Incompressible Elastodynamics in Two Dimensions
• Some Analytical Issues for Elastic Complex Fluids
• Almost global existence for 2-D incompressible isotropic elastodynamics
• Lifespan of solutions of semilinear wave equations in two space dimensions
• Global Existence of Strong Solution for Equations Related to the Incompressible Viscoelastic Fluids in the Critical $L^p$ Framework
• The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions
• LOCAL ENERGY DECAY FOR SOLUTIONS OF MULTI-DIMENSIONAL ISOTROPIC SYMMETRIC HYPERBOLIC SYSTEMS
• Almost global existence to nonlinear wave equations in three space dimensions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Almost global existence of elastic waves of finite amplitude arising from small initial disturbances
• Blow-up for quasi-linear wave equations in three space dimensions
• A Damped Hyperbolic Equation on Thin Domains
• The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
• Global existence for three‐dimensional incompressible isotropic elastodynamics via the incompressible limit
• Global Small Amplitude Solutions of Nonlinear Hyperbolic Systems with a Critical Exponent under the Null Condition
• Global Well-Posedness for Viscoelastic Fluid System in Bounded Domains
• Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions
• Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions
• Nonlinear Wave Equations
• Global existence for three‐dimensional incompressible isotropic elastodynamics
• On the initial‐boundary value problem of the incompressible viscoelastic fluid system
• Global Existence of Classical Solutions for the Two-Dimensional Oldroyd Model via the Incompressible Limit
• On hydrodynamics of viscoelastic fluids
• Some results on the Navier-Stokes equations in thin 3D domains
• The null condition for quasilinear wave equations in two space dimensions. I