A priori estimates and analytical construction of radially symmetric solutions in the gas dynamics

Magali Lécureux-Mercier (1)

1 UCBL - Université Claude Bernard Lyon 1

In this article we derive C^1-a priori estimates on the Riemann invariants of the Euler compressible equations in the case of cylindrical or spherical symmetry. These estimates allow then to construct shock waves with a time of existence proportional to the distance to the origin at the initial time.

Mots clés: long time of existence; Euler compressible equations; shock wave solution; long time of existence.

Domaines: Equations aux dérivées partielles [math.AP]

Magali Lécureux-Mercier. A priori estimates and analytical construction of radially symmetric solutions in the gas dynamics. 2013. ⟨hal-00849107v3⟩