Zero-noise solutions of linear transport equations without uniqueness: An example

DOI10.1016/j.crma.2009.04.027zbMath1167.35006OpenAlexW2013771267MaRDI QIDQ1028078

Franco Flandoli, Stefano Attanasio

Publication date: 30 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.crma.2009.04.027

zbMATH Keywords

zero-noise limitmultiplicative noise perturbation

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for linear first-order PDEs (35F10)

Related Items (14)

Stochastic regularization effects of semi-martingales on random functions ⋮ Noise Prevents Collapse of Vlasov-Poisson Point Charges ⋮ On a selection problem for small noise perturbation in the multidimensional case ⋮ On the convergence of stochastic transport equations to a deterministic parabolic one ⋮ On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations ⋮ Well-posedness by noise for scalar conservation laws ⋮ Uniqueness for a stochastic inviscid dyadic model ⋮ Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations ⋮ Smooth approximation is not a selection principle for the transport equation with rough vector field ⋮ On regularization by a small noise of multidimensional odes with non-Lipschitz coefficients ⋮ Selection of equilibria in a linear quadratic mean-field game ⋮ The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions ⋮ ‘Life after death’ in ordinary differential equations with a non-Lipschitz singularity ⋮ A zero-noise limit to a symmetric system of conservation laws

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• A note on generalized flows
• Phénomène de Peano et grandes déviations
• Small random perturbations of peano phenomena
• Generalized calculus and sdes with non regular drift
• A singular large deviations phenomenon

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