Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation
Cyril Imbert, Tianling Jin, Roman Shvydkoy
TL;DR
This paper derives Schauder estimates for a broad class of linear integro-differential equations and applies these results to establish global well-posedness for a non-local Burgers equation.
Contribution
It provides new Schauder estimates for integro-differential equations and extends global well-posedness results to a non-local Burgers equation.
Findings
Established Schauder estimates for linear integro-differential equations.
Proved global well-posedness for a scalar non-local Burgers equation.
Abstract
We obtain Schauder estimates for a general class of linear integro-differential equations. The estimates are applied to a scalar non-local Burgers equation and complete the global well-posedness results obtained in \cite{ISV}.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Navier-Stokes equation solutions