Low-regularity well-posedness for the ZK equation on a half-strip

Studied here is the Zakharov–Kuznetsov equation with a linear transport term posed on a half-strip with nonhomogeneous boundary condition. Using Bourgain-type spaces adapted to the ZK dispersive structure, anisotropic smoothing and boundary trace estimates, we establish its local well-posedness in $L^2\mathrm{.}$