In this paper, we establish the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data in the space L ¹_loc . The hypotheses on the initial data may be the least requirement to ensure the existence of a weak solution in the Lebesgue measurable sense. The novelty and also the essence of the difficulty of the problem lie in the fact that we have neither the requirement on the local boundedness of the density nor that which is bounded away from vacuum. We develop the previous results on this degenerate system. The method used is Lagrangian representation, the essence of which is characteristic analysis. The key point is to prove the existence of the Lagrangian representation and the absolute continuity of the potentials constructed with respect to the space and the time variables. We achieve this by finding a property of the fundamental theorem of calculus for Lebesgue integration, which is a sufficient and necessary condition for judging whether a monotone continuous function is absolutely continuous. The assumptions on the initial data in this paper are believed to also be necessary for ruling out the formation of Dirac singularity of density. The ideas and techniques developed here may be useful for other nonlinear problems involving similar difficulties.

在本文中，我们建立了L ¹ _loc空间中具有大量初始数据的Chaplygin气体的一维可压缩等熵欧拉系统的柯西问题解的整体存在性和唯一性 。初始数据上的假设可能是确保在Lebesgue可测量的意义上确保弱解存在的最低要求。问题的新颖性和实质在于，我们既不需要密度的局部有界性，也不需要真空约束。我们在这个退化的系统上开发了以前的结果。使用的方法是拉格朗日表示法，其本质是特征分析。关键是要证明拉格朗日表示的存在以及相对于空间和时间变量构造的势的绝对连续性。我们通过找到Lebesgue积分的微积分基本定理的性质来实现这一点，这是判断单调连续函数是否绝对连续的充分必要条件。据信，对初始数据的假设对于排除密度Dirac奇异点的形成也是必要的。这里提出的思想和技术可能对涉及类似困难的其他非线性问题很有用。