Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

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. We consider the two-dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for s ≥ 3 4 , the water waves system is locally well-posed in ℋ s , which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru. It is also a 1 4 improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru.