Well-Posedness in Variable-Exponent Function Spaces for the Three-Dimensional Micropolar Fluid Equations
Muhammad Zainul Abidin, Muhammad Marwan, Naeem Ullah, Ahmed M. Zidan
Abstract
In this paper, we work on the Cauchy problem of the three-dimensional micropolar fluid equations. For small initial data, in the variable-exponent Fourier–Besov spaces, we achieve the global well-posedness result. The Littlewood–Paley decomposition method and the Fourier-localization technique are main tools to obtain the results. Moreover, the results discussed in our work show the Gevrey class regularity of solution to the Cauchy problem of micropolar fluid equations.
Topics & Concepts
MathematicsMathematical analysisCauchy distributionInitial value problemFourier transformWork (physics)Variable (mathematics)Cauchy problemExponentFunction (biology)PhysicsEvolutionary biologyPhilosophyThermodynamicsBiologyLinguisticsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations