Abstract
ABSTRACTIn this paper, we study the compressible isothermal Euler equations with non-vacuum initial data. First, we prove the property of finite propagation to this Cauchy problem by using local energy estimates. Second, we establish the blowup results of the multi-dimensional case in radial symmetry and the one-dimensional case in non-radial symmetry by making assumptions on the initial velocity. Third, we present the blowup results of the three-dimensional case in non-radial symmetry by making assumptions on the initial momentum.
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