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Constantin, P. (2001) Some Open Problems and Research Directions in the Mathematical Study of Fluid Dynamics, Mathematics Unlimited-2001 and Beyond. Springer Verlag, Berlin, 353-360.

has been cited by the following article:

• TITLE: Classical Fundamental Unique Solution for the Incompressible Navier-Stokes Equation in RN

  AUTHORS: Waleed S. Khedr

  KEYWORDS: Fluid Mechanics, Navier-Stokes Equation, Fundamental Solutions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.4, April 30, 2017

  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 assumptions on the data.