2017
DOI: 10.4236/jamp.2017.54083
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Classical Fundamental Unique Solution for the Incompressible Navier-Stokes Equation in R<sup><i>N</i></sup>

Abstract: We present a class of non-convective classical solutions for the multidimensional incompressible Navier-Stokes equation. We validate such class as a representative for solutions of the equation in bounded and unbounded domains by investigating the compatibility condition on the boundary, the smoothness of the solution inside the domain and the boundedness of the energy. Eventually, we show that this solution is indeed the unique classical solution for the problem given some appropriate and convenient assumptio… Show more

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Cited by 3 publications
(1 citation statement)
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“…It remains to answer the question whether there exists another possible solution to Model Equation (5) in the sense of Definition 2.1. The orthogonality argument presented in [KW,Theorem 4] to prove uniqueness remains valid in the context of this article. It simply depends on the coincidence of any possible solutions on the boundary.…”
Section: Resultsmentioning
confidence: 84%
“…It remains to answer the question whether there exists another possible solution to Model Equation (5) in the sense of Definition 2.1. The orthogonality argument presented in [KW,Theorem 4] to prove uniqueness remains valid in the context of this article. It simply depends on the coincidence of any possible solutions on the boundary.…”
Section: Resultsmentioning
confidence: 84%