Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption
Wei‐Xi Li, Nader Masmoudi, Tong Yang
Abstract
Abstract We establish the well‐posedness in Gevrey function space with optimal class of regularity 2 for the three‐dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three‐dimensional instabilities in the system leading to ill‐posedness are not worse than the two‐dimensional ones. © 2021 Wiley Periodicals LLC.
Topics & Concepts
Prandtl numberMathematicsSpace (punctuation)Function (biology)Mathematical analysisFunction spaceApplied mathematicsClass (philosophy)Computer scienceConvectionMechanicsPhysicsOperating systemEvolutionary biologyBiologyArtificial intelligenceAdvanced Mathematical Physics ProblemsNavier-Stokes equation solutionsStability and Controllability of Differential Equations