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.