Exact and approximate expressions are established for dissipation, the power of the shear stress at the wall and the boundary layer thickness corresponding to the motion of an Oldroyd-B fluid induced by a constantly accelerating plate. The similar expressions for Maxwell, Newtonian and second grade fluids, performing the same motion, are obtained as limiting cases of our general results. The sp...

For the two-species Vlasov-Maxwell-Boltzmann (VMB) system with scaling under which moments of fluctuations to global Maxwellians formally converge two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) Ohm's law, we prove uniform estimates respect Knudsen number $\eps$ for fluctuations. As consequences, existence in time classical solutions VMB all $\eps \in (0,1]$ is established. Furthe...

The fundamental “two-fluid” model for describing plasma dynamics is given by the EulerMaxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to globa...

Maxwell accounted for the apparent elastic behavior of the electromagnetic field through augmenting Ampere’s law by the so-called displacement current much in the same way that he treated the viscoelasticity of gases. Original Maxwell constitutive relations for both electrodynamics and fluid dynamics were not material invariant, while combining Faraday’s law and the Lorentz force makes the firs...