Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy
نویسندگان
چکیده
We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity (−Δ)θ, where 0≤θ<1. The proof consists of a convex integration scheme new building blocks 2D intermittency and suitable temporal correctors, are motivated by inherent geometric structure viscoelastic equations.
منابع مشابه
Weak Solutions for One-dimensional Non-convex Elastodynamics
We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in elastic bars proposed by Ericksen [19]. The instantaneous formation of microstructures of local weak solutions is observed for all smooth initial data with i...
متن کاملConvergence of variational approximation schemes for three dimensional elastodynamics with polyconvex energy
We consider a variational scheme developed in [10] that approximates the equations describing the dynamics of three dimensional motions for isotropic elastic materials; these form a system of conservation laws. We establish the convergence of the time-continuous interpolates constructed in the scheme to a smooth solution of the elastodynamics system by adapting the relative entropy method to th...
متن کاملMixed Methods for Elastodynamics with Weak Symmetry
We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weakly imposed symmetry of stress. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces...
متن کاملWeak Finite Dimensional Approximations
We make a formal study of the diierential equation u rr + 2 r u r + u + u 5+" = 0; u r (0) = u(1) = 0; u > 0 if 0 6 r < 1 (1) when posed as a variational problem over a nite dimensional subset S h of H 1 0 comprising piecewise linear functions deened on a mesh of size h. We determine critical points U h 2 S h of the variational form of (1). Such functions are perturbations of u when a solution ...
متن کاملThree-dimensional kinematics and limb kinetic energy of running cockroaches.
We tested the hypothesis that fast-running hexapeds must generate high levels of kinetic energy to cycle their limbs rapidly compared with bipeds and quadrupeds. We used high-speed video analysis to determine the three-dimensional movements of the limbs and bodies of cockroaches (Blaberus discoidalis) running on a motorized treadmill at 21 cm s-1 using an alternating tripod gait. We combined th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2022
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2022.08.031