Generalized solutions to linearized equations of thermoelastic solid and viscous thermofluid

Abstract

Within the framework of continuum mechanics, the full description of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy balance equations, the first and the second laws of thermodynamics, and an additional set of thermomechanical state laws. The present paper is devoted to the investigation of this system. Assuming that variations of the physical characteristics of the thermomechanical system of the fluid and the solid are small about some rest state, we derive the linearized non-stationary dynamical model, prove its well-posedness, establish additional refined global integral bounds for solutions, and further deduce the linearized incompressible models and models incorporating absolutely rigid skeleton, as asymptotic limits.

Keywords

• Thermoelastic solid
• viscous thermofluid
• compressibility
• linearization
• existence and uniqueness theory
• weak generalized solutions.