A sufficient condition for the existence of smooth solutions of the relativistic cold plasma equations on any given time interval

2025/10/18 by Rozanova, Olga S., Chizhonkov, Evgeniy V.
#35Q60 35L60 35L67 34M10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.16613

Abstract

In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such sufficient conditions take into account the smallness properties of not only the derivatives of the initial data but also the initial data themselves. The accuracy of the obtained initial condition is investigated using a numerical experiment. The structure of the emerging singularities is also studied.

Citations

• Criterion of singularity formation for radial solutions of the pressureless Euler-Poisson equations in exceptional dimension
• The repulsive Euler-Poisson equations with variable doping profile

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