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Blow-up of the spherically symmetric solutions of the 2-D full compressible Euler equations. (Chinese. English summary) Zbl 1349.35281

Summary: In this paper, we are concerned with the blow-up problem of the spherically symmetric solutions to the 2-D full compressible Euler system. When the initial data are of small perturbations with respect to a constant state, we obtain the precise bound of the lifespan. With compact simporf for the 2-D isentropic Euler system with the symmetric rotation, previous researcher has established the lifespan of the small data symmetric solutions. Our focus is on the non-isentropic case in this paper. The main ingredients are: at first we construct a suitable approximate solution, then by utilizing the norms for studying the 3-D blow-up problems and combining some delicate analysis, we obtain the precise lower bound of the lifespan. Finally we show that the lower bound is also the upper bound of the lifespan by exploiting some techniques in ordinary differential equations.

MSC:

35Q31 Euler equations
35B06 Symmetries, invariants, etc. in context of PDEs
35B44 Blow-up in context of PDEs
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