Energy-based stability estimates for incompressible media with tensor-nonlinear constitutive relations

被引:0
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作者
Dimitri Georgievskii
Vakhtang Putkaradze
机构
[1] Lomonosov Moscow State University,Mechanical and Mathematical Department
[2] Leninskie Gory,Moscow Center for Fundamental and Applied Mathematics
[3] Lomonosov Moscow State University,Department of Mathematical and Statistical Sciences
[4] Leninskie Gory,undefined
[5] University of Alberta,undefined
关键词
Continuum mechanics; Stress–strain relationships; Stability; Small deviations; Energy-based estimates; Variational inequalities;
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摘要
Tensor-nonlinear media are generalized models of continua having nonlinear relationship between the stress and strain rate, important for the descriptions of, for example, non-Newtonian fluids. We consider a wide class of such tensor-nonlinear, isotropic, incompressible media, which may possess a scalar stress potential in terms of velocity gradients, i.e., the analogue or Raleigh function. We also provide a setting of several linearized problems for these media in moving three-dimensional domains. Energy-based estimates and subsequent Lyapunov, asymptotic and exponential stability results are derived through an application of a sequence of integral inequalities. We also present particular cases of stability estimates for a variety of tensor-linear, or quasilinear, media that may or may not possess the dissipation potential, such as the Bingham and Saint-Venant media, or Newtonian viscous fluid.
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页码:1403 / 1415
页数:12
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