On a class of forced active scalar equations with small diffusive parameters

2020/11/16 by Susan Friedlander, Friedlander, Susan, Anthony Suen +1
Engineering · Mathematics · #35Q35 #76D03 #76W05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2011.08454

openalex publication_date 2020/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial differential equations often contain several small parameters. We study a general class of such PDEs called active scalar equations which in specific parameter regimes produce certain well known models for fluid motion. We address various mathematical questions relating to well-posedness, regularity and long time behaviour of the solutions to this general class including vanishing limits of several diffusive parameters.

Citations

• Gevrey class regularity for the solutions of the Navier-Stokes equations

Related

• Non-uniqueness of forced active scalar equations with even drift operators
• Ill/well-posedness of non-diffusive active scalar equations with physical applications
• Regularity and blow up for active scalars
• Operator splitting for well-posed active scalar equations
• Convex integration for a class of active scalar equations