Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications

Susan FRIEDLANDER, Chun Kit Anthony SUEN

Research output: Contribution to journalArticles

Abstract

This paper considers a family of non-diffusive active scalar equations where a viscosity type parameter enters the equations via the constitutive law that relates the drift velocity with the scalar field. The resulting operator is smooth when the viscosity is present but singular when the viscosity is zero. We obtain Gevrey-class local well-posedness results and convergence of solutions as the viscosity vanishes. We apply our results to two examples that are derived from physical systems: firstly a model for magnetostrophic turbulence in the Earth’s fluid core and secondly flow in a porous media with an “effective viscosity”. Copyright © 2019 Springer Nature Switzerland AG.
Original languageEnglish
Article number50
JournalJournal of Mathematical Fluid Mechanics
Volume21
Issue number4
Early online date09 Sep 2019
DOIs
Publication statusPublished - Dec 2019

Citation

Friedlander, S., & Suen, A. (2019). Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications. Journal of Mathematical Fluid Mechanics, 21(4). Retrieved from https://doi.org/10.1007/s00021-019-0454-1

Keywords

  • Active scalar equations
  • Vanishing viscosity limit
  • Gevrey-class solutions

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