Long‐Time Instability of the Couette Flow in Low Gevrey Spaces
Yu Deng, Nader Masmoudi
Abstract
Abstract We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
Topics & Concepts
Inviscid flowInstabilityMathematicsFlow (mathematics)Nonlinear systemSpace (punctuation)Mathematical analysisCouette flowStability (learning theory)Class (philosophy)MechanicsGeometryPhysicsComputer scienceArtificial intelligenceMachine learningOperating systemQuantum mechanicsFluid Dynamics and Turbulent FlowsNavier-Stokes equation solutionsStability and Controllability of Differential Equations