Abstract
This paper considers a pressureless Euler-Poisson system with viscosity in plasma physics in the torus . We give a rigorous justification of its asymptotic limit toward the incompressible Navier Stokes equations via quasi-neutral regime using the modulated energy method.
Highlights
We will consider the following system:∂tu u · ∇ u μΔu ∇V,∂tn div n u 0, ΔV n −, for x ∈ T3 and t > 0, n ∈ R, u ∈ R2. is small parameter and μ > 0 is a constant viscosity coefficient
This paper considers a pressureless Euler-Poisson system with viscosity in plasma physics in the torus T3
UNS is a solution of the incompressible Navier-Stokes equations
Summary
Is small parameter and μ > 0 is a constant viscosity coefficient. To solve uniquely the Poisson equation, we add the T3 n dx 1. Passing to the limit when → 0, it is easy to see, at least at a very formal level, that n , u tends to nNS, uNS , where nNS 1 and. ∂tuNS uNS · ∇ uNS μΔuNS ∇VNS, 1.2 div uNS 0
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