Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions

DOI10.1137/15M1007380zbMath1343.35060arXiv1412.6387OpenAlexW3102950310MaRDI QIDQ3460260

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Publication date: 7 January 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6387

zbMATH Keywords

superposition principlerenormalizationtransport equationcontinuity equationLipschitz functionsdisintegration of measuresuniqueness of bounded solutions

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Initial value problems for linear first-order PDEs (35F10) Integration and disintegration of measures (28A50) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (9)

Differentiability properties of the flow of 2d autonomous vector fields ⋮ A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients ⋮ On the one-dimensional continuity equation with a nearly incompressible vector field ⋮ Lagrangian representations for linear and nonlinear transport ⋮ On the Extreme Points of the Unit Ball in the Space of Solenoidal Vector Measures on the Plane ⋮ Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications ⋮ A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\) ⋮ On the structure of divergence-free measures on \(\mathbb{R}^2\) ⋮ Differentiability in measure of the flow associated with a nearly incompressible BV vector field

Cites Work

• Steady nearly incompressible vector fields in two-dimension: chain rule and renormalization
• Differential equations with singular fields
• Transport equation and Cauchy problem for BV vector fields
• Traces and fine properties of a \(BD\) class of vector fields and applications
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• A system of non-strictly hyperbolic conservation laws arising in elasticity theory
• A uniqueness result for the continuity equation in two dimensions
• An ill-posed Cauchy problem for a hyperbolic system in two space dimensions
• LAGRANGIAN FLOWS FOR VECTOR FIELDS WITH GRADIENT GIVEN BY A SINGULAR INTEGRAL
• Well-Posedness for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions
• Estimates and regularity results for the DiPerna-Lions flow
• On the theory of divergence-measure fields and its applications
• Structure of level sets and Sard-type properties of Lipschitz maps
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