Global solutions of a surface quasigeostrophic front equation
John K. Hunter, Jingyang Shu, Qingtian Zhang
Abstract
We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth solution under a convergence condition on the multilinear expansion of the nonlinear term in the equation, and, for sufficiently smooth and small initial data, we prove that the solution is global.
Topics & Concepts
Initial value problemMultilinear mapConvergence (economics)Mathematical analysisNonlinear systemDimension (graph theory)MathematicsSurface (topology)Geostrophic windFront (military)Space (punctuation)Term (time)PhysicsGeometryPure mathematicsComputer scienceMechanicsMeteorologyEconomicsEconomic growthOperating systemQuantum mechanicsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsGeometric Analysis and Curvature Flows