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For one dimensional or multidimensional compressible Euler system ofpolytropic gases, it is well known that the smooth solution will generallydevelop singularities in finite time. However, for three dimensional Chaplygingases, due to the crucial role of "null condition" in the potential equationwhich is derived by the irrotational and isentropic flow, P.Godin in [9] hasproved the global existence of a smooth 3-D spherically symmetric flow withvariable entropy when the initial data are of small smooth perturbations withcompact supports to a constant state. It is noted that there are some essentialdifferences on the global solution or blowup problems between 2-D and 3-Dhyperbolic systems. In this paper, we will focus on the global symmetricsolution problem of 2-D full compressible Euler system of Chaplygin gases.Through carrying out involved analysis and finding an appropriate weight we canderive some uniform weighted energy estimates on the small symmetric solutionto 2-D compressible Euler system of Chaplygin gases and further establish theglobal existence of smooth solution by continuous induction method.

The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases