arXiv subjects

Faris A. El-Katri

Publications and source records attributed to Faris A. El-Katri.

3 recordsLinked to original sources

arXiv2026

Existence and singularity formation for the supersonic expanding wave of radially symmetric non-isentropic compressible Euler equations

This paper studies the existence and singularity formation of supersonic expanding waves for the radially symmetric non-isentropic compressible Euler equations of polytropic gases. We introduce a suitable pair of gradient variables to characterize the rarefaction and compression properties of the solutions. Based on their Riccati equations, we construct several useful invariant domains to establish a series of priori estimates of solutions under some assumptions on the initial data. We show that the solution is smooth in the characteristic triangle or quadrangle domain if both of these two gradient variables are non-negative at the initial time. On the other hand, when one of these two variables is very negative at some initial point, the solution forms a singularity in finite time.

math.AP↗

arXiv2025

Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry

In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the invariant domain idea, we show that, for polytropic ideal gases with $γ\geq3$, the smooth solution develops a singularity in finite time for a class of initial supersonic inward waves.

math.AP↗

arXiv2024

Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry

In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new definition, we show that solutions with rarefaction initial data will not form shock in finite time, i.e. exist global-in-time as classical solutions. On the other hand, singularity forms in finite time when the initial data include strong compression somewhere. Several useful invariant domains will be also given.

math.AP↗