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Formation of singularities in compressible fluids in two-space dimensions. (English) Zbl 0692.35015
The author studies the solution of the two-dimensional Euler equations for a polytropic ideal fluid; the associated Cauchy data are considered sufficiently regular to ensure the local existence of the solution and are constant outside a sphere of radius R. Moreover, the front of the initial disturbance satisfies certain positivity conditions. Under these assumptions, it is proved that any local $$C^ 1$$-solution of the considered problem, regardless of the size of the initial disturbance, will develop singularities in finite time.
Reviewer: I.Toma

##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35Q05 Euler-Poisson-Darboux equations 35L45 Initial value problems for first-order hyperbolic systems 35L67 Shocks and singularities for hyperbolic equations
##### Keywords:
blow up; initial disturbance
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##### References:
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