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

Waleed S. Khedr
2017 Journal of Applied Mathematics and Physics  
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
more » ... ppropriate and convenient assumptions on the data.
doi:10.4236/jamp.2017.54083 fatcat:vc6uf4mxtfcuhhun4hxvikq5li