Curved-pipe flow with boundary conditions involving Bernoulli pressure

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In this article, we study the steady-state flow of the incompressible viscous fluid through a thin distorted pipe with an arbitrary central curve. We prescribe the inflow and outflow boundary conditions involving the Bernoulli pressure with a given pressure drop. Using the multiscale expansion technique with respect to the pipe's thickness, we construct the higher-order asymptotic approximation of the flow given by the explicit formulae for the velocity and pressure. We also perform a detailed error analysis justifying the usage of the proposed solution and indicating its order of accuracy. For more information see https://ejde.math.txstate.edu/Volumes/2024/63/abstr.html