A note on transport equation in quasiconformally invariant spaces

DOI10.1515/acv-2016-0003zbMath1387.49040arXiv1512.03650OpenAlexW2963990831MaRDI QIDQ1707965

Albert Clop, Joan Orobitg, Joan Mateu, Ren Jin Jiang

Publication date: 4 April 2018

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03650

zbMATH Keywords

transport equationvector fieldsquasiconformal mappingbounded mean oscillation (BMO) space

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sensitivity, stability, well-posedness (49K40) Linear first-order PDEs (35F05) Existence theories for problems in abstract spaces (49J27) Existence theories for optimal control problems involving partial differential equations (49J20) Initial value problems for linear first-order PDEs (35F10) Euler equations (35Q31)

Related Items (7)

Pointwise descriptions of nearly incompressible vector fields with bounded curl ⋮ Well-posedness for the continuity equation for vector fields with suitable modulus of continuity ⋮ Nonlinear transport equations and quasiconformal maps ⋮ Classical flows of vector fields with exponential or sub-exponential summability ⋮ Sobolev regular flows of non-Lipschitz vector fields ⋮ The transport equation in the scaling invariant Besov or Essén-Janson-Peng-Xiao space ⋮ FLOW WITH DENSITY AND TRANSPORT EQUATION IN

Cites Work

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• Flows for non-smooth vector fields with subexponentially integrable divergence
• On the global well-posedness for Euler equations with unbounded vorticity
• Pointwise characterizations of Besov and Triebel-Lizorkin spaces and quasiconformal mappings
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Funktionen beschränkter mittlerer Oszillation
• Ordinary differential equations and quasiconformal mappings
• Functions of bounded mean oscillation and quasiconformal mappings
• Uniqueness theorem for the basic nonstationary problem in the dynamics on an ideal incompressible fluid
• Logarithmic potentials, quasiconformal flows, and \(Q\)-curvature
• Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces
• Flows associated with irregular \(\mathbb R^d\)-vector fields
• Vorticity and Incompressible Flow
• On the global well-posedness of the 2D Euler equations for a large class of Yudovich type data

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