Optimal decay rate of the two-fluid incompressible Navier–Stokes–Fourier–Poisson system with Ohm’s law

2022 ◽  
Vol 63 ◽  
pp. 103392
Author(s):  
Weihua Gong ◽  
Fujun Zhou ◽  
Weijun Wu ◽  
Qian Hu
Keyword(s):  
Decay Rate ◽  
Navier Stokes ◽  
Poisson System ◽  
Ohm’S Law ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Ohm's Law ◽  
Two Fluid

scholarly journals Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations

2013 ◽  
Vol 143 (5) ◽  
pp. 905-927 ◽  
Author(s):  
Margaret Beck ◽  
C. Eugene Wayne
Keyword(s):  
Decay Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Long Time ◽  
High Reynolds

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows, where they often emerge on timescales much shorter than the viscous timescale, and then dominate the dynamics for very long time intervals. In this paper we propose a dynamical systems explanation of the metastability of an explicit family of solutions, referred to as bar states, of the two-dimensional incompressible Navier–Stokes equation on the torus. These states are physically relevant because they are associated with certain maximum entropy solutions of the Euler equations, and they have been observed as one type of metastable state in numerical studies of two-dimensional turbulence. For small viscosity (high Reynolds number), these states are quasi-stationary in the sense that they decay on the slow, viscous timescale. Linearization about these states leads to a time-dependent operator. We show that if we approximate this operator by dropping a higher-order, non-local term, it produces a decay rate much faster than the viscous decay rate. We also provide numerical evidence that the same result holds for the full linear operator, and that our theoretical results give the optimal decay rate in this setting.

A convergence to the Navier–Stokes–Maxwell system with solenoidal Ohm's law from a two-fluid model

2020 ◽  
pp. 1-22
Author(s):  
Zeng Zhang
Keyword(s):  
Electromagnetic Field ◽  
Transfer Coefficient ◽  
Fluid Model ◽  
Navier Stokes ◽  
Maxwell System ◽  
Ohm’S Law ◽  
Momentum Transfer Coefficient ◽  
Ohm's Law ◽  
Two Fluid Model ◽  
Two Fluid

We show the incompressible Navier–Stokes–Maxwell system with solenoidal Ohm's law can be derived from the two-fluid incompressible Navier–Stokes–Maxwell system when the momentum transfer coefficient tends to zero. The strategy is based on the decay and dissipative properties of the electromagnetic field.

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