Solving large classes of nonlinear systems of PDEs

It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff continuous functions. The usual NavierStokes equations, as well as their various modifications are included as particular cases. The solution method does not involve functional analysis, nor various Sobolev or other spaces of distributions or generalized functions. The general and type independent existence and regularity results regarding solutions presented here are a first in the literature. ”... provided also if need be that the notion of a solution shall be suitably extended ...” cited from Hilbert’s 20th Problem 1. Main ideas of the order completion solution method The solution method is divided in two parts. The proof of the existence of solutions follows the method of order completion introduced and first developed in Oberguggenberger & Rosinger. The proof of the