On singular vortex patches, II: Long-time dynamics
Tarek M. Elgindi, In‐Jee Jeong
Abstract
In a companion paper [arXiv:1903.00833], we gave a detailed account of the well-posedness theory for singular vortex patches. Here, we discuss the long-time dynamics of some of the classes of vortex patches we showed to be globally well-posed in the above-mentioned paper. In particular, we give examples of time-periodic behavior, cusp formation in infinite time at an exponential rate, and spiral formation in infinite time.
Topics & Concepts
MathematicsVortexDynamics (music)Cusp (singularity)Exponential functionSpiral (railway)Mathematical analysisExponential growthClassical mechanicsGeometryPhysicsMechanicsAcousticsNavier-Stokes equation solutionsGeometric Analysis and Curvature FlowsAdvanced Mathematical Physics Problems