Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space
Abstract
Based on the essential connection of the parabolic inertia Lam\'e equations and Navier-Stokes equations, we prove the existence of smooth solutions of the incompressible Navier-Stokes equations in three-dimensional Euclidean space R3 by showing the existence and uniqueness of smooth solutions of the parabolic inertia Lam\'e equations and by letting a Lam\'e constant λ tends to infinity (the other Lam\'e constant μ>0 is fixed).
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