We investigate the local and global well-posedness of the kinetic derivative nonlinear Schrödinger equation(KDNLS) on \({{\mathbb {R}}}\) , described by \(\begin{aligned} i\partial _t u + \partial _x^2 u = i\alpha \partial _x (|u|^2 u) + i\beta \partial _x ({\mathcal {H}}(|u|^2) u), \end{aligned}\) where \(\alpha , \beta \in \mathbb {R}\) , and \({\mathcal {H}}\) represents the Hilbert transformation. For KDNLS, the \(L^2\) norm of a solution is decreasing (resp. increasing, conserved) when \(\beta \) is negative (resp. positive, zero). Focusing on the Sobolev spaces \(H^2\) and \(H^2 \cap H^{1,1}\) , we establish local well-posedness via the energy method combined with gauge transformations to address resonant interactions in both cases of negative and positive \(\beta \) . For the dissipative case \(\beta < 0\) , we further demonstrate global well-posedness by deriving an a priori bound in \(H^2\) .
