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Stability of the rarefaction wave for a two-fluid plasma model with diffusion. (English) Zbl 1362.35038

The authors study the Cauchy problem on the whole line of a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data. Since they are interested in the behaviour in the large for the quasineutral Euler equation in the setting of the rarefaction wave, they assume that both the asymptotic densities \(n_{e,\pm}=n_{i,\pm}\) and the asymptotic velocities \(u_{e,\pm}=u_{i,\pm}\) are the same for both fluids (\(e\) are electrons and \(i\) ions) and for both limits \((x\to\pm \infty)\). They prove the uniqueness of the global solution with prescribed asymptotics under the restrictive assumption that the asymptotic ratio of the thermal speeds of ions and electrons is not less than \(1/2\). To prove the main theorem they use the energy method.

MSC:

35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q35 PDEs in connection with fluid mechanics
82D10 Statistical mechanics of plasmas
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q31 Euler equations
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References:

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