A new formulation for the linearized Navier-Stokes equation - Yousra, Ouali; Younes, A. (International Journal of Applied Mathematical Research, 2014)
This paper is devoted to study the Navier-Stokes equations by applying the curl and using a current function, weobtain a non-linear biharmonic problem where the pressure disappears and instead of the velocity, we are workingwith a scalar function. After a linearization, we obtain a sequence of linear problems. We study the existence anduniqueness of its solutions. Finally we show the convergence of the sequence of the linearized problems obtained tothe non-linear one.Keywords: Bi-Laplacian, Existence and uniqueness, Navier-Stokes equations.