Parabolic bootstrap for some non-linear equations
Igor Honor\'e (UCBL, ICJ)
TL;DR
This paper establishes well-posedness and Schauder estimates for certain non-linear PDE systems, proving the existence and uniqueness of smooth solutions for a novel non-local semi-incompressible Navier-Stokes equation in three dimensions.
Contribution
It introduces a parabolic bootstrap method for non-linear equations and demonstrates global smooth solutions for a new non-local Navier-Stokes model.
Findings
Proved well-posedness and Schauder estimates for a class of PDE systems.
Established existence and uniqueness of global smooth solutions for the semi-incompressible Navier-Stokes equation.
Developed a parabolic bootstrap approach for non-linear PDE analysis.
Abstract
We obtain the well-posedness and Schauder estimates for a class of system of linear, quasi-linear and non-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and non-local equation that we call "semi" incompressible Navier Stokes equation in R 3 .
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Physics Problems · Navier-Stokes equation solutions