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The two-dimensional wave-breaking of relativistic plasma waves driven by a ultrashort high-power lasers, is described within a framework of cold 2-D fluid theory. It is shown that the transverse nonlinearity of the plasma wave results in temporally increasing transverse plasma oscillation in the wake of the laser pulse, inevitably inducing wave-breaking below the 1-D threshold. A condition for wavebreaking is obtained and evaluated. A preformed density channel is found to partially cancel the effect and increase the length of wakefield that survives before wavebreaking occurs.