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In this paper, we will solve the Leray's problem for the stationaryNavier-Stokes system in a 2D infinite distorted strip with the Navier-slipboundary condition. The existence, uniqueness, regularity and asymptoticbehavior of the solution will be investigated. Moreover, we discuss how thefriction coefficient affects the well-posedness of the solution. Due to thevalidity of the Korn's inequality, all constants in each a priori estimate areindependent of the friction coefficient. The main novelty is the total flux ofthe velocity can be relatively large (proportional to the {\it slip length})when the friction coefficient of the Navier-slip boundary condition is small,which is essentially different from the 3D case.

Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition