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This paper derives a solution to the Navier–Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier–Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier–Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary.

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