Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
Tristan Buckmaster, Maria Colombo, Vlad Vicol
Abstract
We prove non-uniqueness for a class of weak solutions to the Navier–Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.
Topics & Concepts
MathematicsHausdorff dimensionBounded functionUniquenessHausdorff measureVorticityMathematical analysisMinkowski–Bouligand dimensionDimension (graph theory)Navier–Stokes equationsHausdorff spaceIntegrable systemClass (philosophy)Hausdorff distancePure mathematicsFractal dimensionFractalVortexPhysicsCompressibilityThermodynamicsComputer scienceArtificial intelligenceNavier-Stokes equation solutionsFluid Dynamics and Turbulent FlowsNonlinear Partial Differential Equations