Log-Lipschitz regularity and uniqueness of the flow for a field in \((W_{\text{loc}}^{n/p+1,p}(\mathbb{R}^n))^n\)

DOI10.1016/S1631-073X(02)02426-3zbMath1022.34002OpenAlexW1599696556MaRDI QIDQ1608672

Enrique Zuazua

Publication date: 30 October 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1631-073x(02)02426-3

zbMATH Keywords

Sobolev spaceslog-Lipschitz regularityPicard-Lindelöfuniqueness of the flow

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12)

Related Items (14)

Log-Lipschitz regularity of the 3D Navier-Stokes equations ⋮ Implicit parametrizations and applications in optimization and control ⋮ Existence and Uniqueness of Multidimensional BSDEs and of Systems of Degenerate PDEs with Superlinear Growth Generator ⋮ Classical flows of vector fields with exponential or sub-exponential summability ⋮ Finite element approximation of the Sobolev constant ⋮ Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel ⋮ Embeddings and characterizations of Lipschitz spaces ⋮ Iterated Hamiltonian type systems and applications ⋮ Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts ⋮ LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID–SOLID INTERACTION ⋮ A uniqueness criterion for ordinary differential equations ⋮ Local controllability to trajectories for non-homogeneous incompressible Navier-Stokes equations ⋮ Implicit functions and parametrizations in dimension three: generalized solutions ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Cites Work

• Ordinary differential equations, transport theory and Sobolev spaces
• On the uniqueness theorem for generalized solutions of initial-boundary problems for the Maguerre-Vlasov vibrations of shallow shells with clamped boundary conditions
• Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations
• Elliptic partial differential equations of second order
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Sur les équations différentielles ordinaires et les équations de transport
• Sobolev imbedding theorems in borderline cases
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