Some interesting class of integrable partial differential equation systems
Joerg Kampen
TL;DR
This paper identifies a broad class of nonlinear PDE systems with guaranteed global regular solutions, and discusses potential applications to the incompressible Navier-Stokes equations.
Contribution
It introduces a new scheme for establishing global regularity for a class of nonlinear PDE systems, including Navier-Stokes.
Findings
Established a class of PDE systems with global regular solutions
Applied the scheme to the incompressible Navier-Stokes equation
Provided insights into the uniqueness limitations of the method
Abstract
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier Stokes equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Fractional Differential Equations Solutions