Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations

DOI10.1016/j.jde.2013.02.012zbMath1321.34020OpenAlexW2082587006MaRDI QIDQ390986

Nicholas Sharples, James C. Robinson

Publication date: 9 January 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2013.02.012

zbMATH Keywords

avoidance of setsdimension printDiPerna-Lions flowgeneralised flowirregular vector fieldnon-autonomous ordinary differential equation

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Qualitative theory for ordinary differential equations (34C99) Fractals (28A80) Nonautonomous smooth dynamical systems (37C60)

Related Items (3)

On solutions of the transport equation in the presence of singularities ⋮ Non-conservation of dimension in divergence-free solutions of passive and active scalar systems ⋮ Dimension prints for continuous functions on the unit square

Cites Work

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• Transport equation and Cauchy problem for BV vector fields
• Lagrangian representation of a flow
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• On vector fields as generators of flows: A counterexample to Nelson's conjecture
• Coordinate \(d\)-dimension prints
• Strict inequality in the box-counting dimension product formulas
• Flows associated with irregular \(\mathbb R^d\)-vector fields
• Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier–Stokes equations
• Estimates and regularity results for the DiPerna-Lions flow
• Dimension prints
• A General Chain Rule for Derivatives and the Change of Variables Formula for the Lebesgue Integral

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