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In this paper, we establish the global existence of smooth solutions to the2-dimensional (2D) compressible isentropic irrotational Euler equations forChaplygin gases with the short pulse initial data introduced by Christodoulou.This is related to the Majda's conjecture on the non-formation of shock wavesof solutions from smooth initial data for multi-dimensional nonlinear symmetricsystems which are totally linearly degenerate. The main ingredients of ouranalysis consist of showing the positivity of the inverse foliation densitynear the outermost conic surface for all time and solving a global Goursatproblem inside the outermost cone. To overcome the difficulties due to theslower time decay rate of the solutions to the 2D wave equation and thelargeness of the solution, we introduce some new auxiliary energies. It isnoted that the methods and results in the paper can be extended to general 2Dquasilinear wave equations satisfying corresponding null conditions for shortpulse initial data.

Global smooth solutions to the 2D isentropic and irrotational Chaplygin gases with a class of large initial data