Three-dimensional supersonic flows of Euler-Poisson system for potential flow

Abstract

<p style="text-indent:20px;">We prove the unique existence of supersonic solutions of the Euler-Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the main framework is similar to [<xref ref-type="bibr" rid="b1">1</xref>], but there are several technical differences to be taken care of vary carefully. And, it is our main goal to treat all the technical differences occurring when one considers a three dimensional supersonic solution of the steady Euler-Poisson system.</p>