Global smooth solutions of 2D quasilinear wave equationswith higher-order null conditions and short pulse initial data

For the short pulse initial datawith a first-order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutionsto 2D quasilinear wave equations with higher-order null conditions. Such kinds of wave equationsinclude 2D relativistic membrane equations, 2D membrane equations,and some 2D quasilinear equations which comefrom the nonlinear Maxwell equations in electromagnetic theory orfrom the corresponding Lagrangian functionals as perturbations of the Lagrangian densities of linear wave operators. The main ingredients of the analysis here include looking for a new good unknown, finding some key identities based on the higher-order null conditions and the resulting null frames, as well as overcoming the difficulties due to the slow decay of solutions to the 2D wave equation, so that the solutions can be estimated precisely.