2005/05/31 by Roumen Anguelov, Anguelov, Roumen, Elemer E Rosinger +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.math/0505674
Preprint
arxiv created 2005/06/07 · arxiv updated 2009/12/01
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 Navier-Stokes equations, as well as their various modifications aiming at a realistic modelling are included as particular cases. The same holds for the critically important constitutive relations in various branches of Continuum Mechanics. 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.