English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is concerned with the large-time behavior of solutions to theCauchy problem on the two-fluid Euler-Maxwell system with collisions wheninitial data are around a constant equilibrium state. The main goal is therigorous justification of diffusion phenomena in fluid plasma at the linearlevel. Precisely, motivated by the classical Darcy's law for the nonconductivefluid, we first give a heuristic derivation of the asymptotic equations of theEuler-Maxwell system in large time. It turns out that both the density and themagnetic field tend time-asymptotically to the diffusion equations withdiffusive coefficients explicitly determined by given physical parameters.Then, in terms of the Fourier energy method, we analyze the linear dissipativestructure of the system, which implies the almost exponential time-decayproperty of solutions over the high-frequency domain. The key part of the paperis the spectral analysis of the linearized system, exactly capturing thediffusive feature of solutions over the low-frequency domain. Finally, undersome conditions on initial data, we show the convergence of the densities andthe magnetic field to the corresponding linear diffusion waves with the rate$(1+t)^{-5/4}$ in $L^2$ norm and also the convergence of the velocities and theelectric field to the corresponding asymptotic profiles given in the sense ofthe geneneralized Darcy's law with the faster rate $(1+t)^{-7/4}$ in $L^2$norm. Thus, this work can be also regarded as the mathematical proof of theDarcy's law in the context of collisional fluid plasma.

Darcy's law and diffusion for a two-fluid Euler-Maxwell system with dissipation