Estimates and regularity results for the DiPerna-Lions flow
From MaRDI portal
Publication:3524788
DOI10.1515/CRELLE.2008.016zbMath1160.34004MaRDI QIDQ3524788
Camillo De Lellis, Gianluca Crippa
Publication date: 15 September 2008
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Dynamics induced by flows and semiflows (37C10) Asymptotic properties of solutions to ordinary differential equations (34D05)
Related Items
Global Weak Solutions of PDEs for Compressible Media: A Compactness Criterion to Cover New Physical Situations, On the weak solvability of the problem of viscoelasticity with memory, Mixing and un-mixing by incompressible flows, On solutions of the transport equation in the presence of singularities, Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels, Critical non-Sobolev regularity for continuity equations with rough velocity fields, The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems, Existence and Uniqueness Results for the Continuity Equation and Applications to the Chromatography System, Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions, A new approach to bounds on mixing, Optimal feedback control problem for inhomogeneous Voigt fluid motion model, Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit, The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients, Advection diffusion equations with Sobolev velocity field, On problem of the dynamics of a viscoelastic medium with memory on an infinite interval, On the commutativity of flows of rough vector fields, Convergence Rates for Upwind Schemes with Rough Coefficients, Cellular mixing with bounded palenstrophy, Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with $L^1$ Vorticity, Bounds on the rate of enhanced dissipation, Well-posedness of the deterministic transport equation with singular velocity field perturbed along fractional Brownian paths, A note on the Lagrangian flow associated to a partially regular vector field, Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids, Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields, Continuity Equation and Characteristic Flow for Scalar Hencky Plasticity, Interaction of finitely-strained viscoelastic multipolar solids and fluids by an Eulerian approach, Singular McKean-Vlasov SDEs: well-posedness, regularities and Wang's Harnack inequality, Exponential Mixing by Shear Flows, Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift, The problem of the flow of one type of non-Newtonian fluid through the boundary of a multiply connected domain, The weak solvability of an inhomogeneous dynamic problem for a viscoelastic continuum with memory, Weak solvability of fractional Voigt model of viscoelasticity, Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type, Exponential mixing for random dynamical systems and an example of Pierrehumbert, Properties of mixing BV vector fields, Strong convergence of the vorticity and conservation of the energy for the α-Euler equations, Lie brackets of nonsmooth vector fields and commutation of their flows, Well-posedness and regularity for a polyconvex energy, Variability of paths and differential equations with \(\mathrm{BV}\)-coefficients, On weak solvability of a flow problem for viscoelastic fluid with memory, Discretizing advection equations with rough velocity fields on non-Cartesian grids, Lagrangian solutions to the transport-Stokes system, Solvability of the initial-boundary value problem for the high-order Oldroyd model, Existence of weak solution to initial-boundary value problem for finite order Kelvin-Voigt fluid motion model, Sub-exponential mixing of generalized cellular flows with bounded palenstrophy, Strong and weak convergence for the averaging principle of DDSDE with singular drift, On the existence of feedback control for one fractional Voigt model, Exponential self-similar mixing by incompressible flows, Multilinear Singular Integral Forms of Christ-Journé Type, Quasi-Invariant Flow Generated by Stratonovich SDE with BV Drift Coefficient, Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case, A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation, Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms, Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres, Strong continuity for the 2D Euler equations, Flow solutions of transport equations, FLOW WITH DENSITY AND TRANSPORT EQUATION IN, The vortex-wave system with gyroscopic effects, Nonlinear Young integrals and differential systems in Hölder media, Investigation of the weak solubility of the fractional Voigt alpha-model, Regularity estimates for the flow of BV autonomous divergence-free vector fields in R2, Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows, Diperna-Lions flow for relativistic particles in an electromagnetic field, On the uniqueness of solutions to continuity equations, Renormalized solutions of the 2D Euler equations, Distribution dependent SDEs driven by additive continuous noise, Differentiability properties of the flow of 2d autonomous vector fields, Flows for non-smooth vector fields with subexponentially integrable divergence, Weak solutions for a bi-fluid model for a mixture of two compressible non interacting fluids, A shell model for optimal mixing, Strong solutions to stochastic differential equations with rough coefficients, Steady nearly incompressible vector fields in two-dimension: chain rule and renormalization, Lagrangian flows for vector fields with anisotropic regularity, Transport equations with integral terms: existence, uniqueness and stability, Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation, Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor, On the Littlewood-Paley spectrum for passive scalar transport equations, Stochastic differential equations with Sobolev drifts and driven by \(\alpha\)-stable processes, Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system, Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications, A quantitative theory for the continuity equation, Stable mixing estimates in the infinite Péclet number limit, On a maximal inequality and its application to SDEs with singular drift, Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations, Differential equations with singular fields, Stochastic Lagrangian particle approach to fractal Navier-Stokes equations, Lagrangian solutions to the Vlasov-Poisson system with \(L^1\) density, Regularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spaces, Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients, Global existence of weak solutions to the FENE dumbbell model of polymeric flows, Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients, Lagrangian solutions to the 2D Euler system with \(L^1\) vorticity and infinite energy, A new proof of the uniqueness of the flow for ordinary differential equations with \(BV\) vector fields, Lagrangian flows and the one-dimensional Peano phenomenon for ODEs, Lagrangian solutions to the Vlasov-Poisson system with a point charge, Propagation of chaos for the 2D viscous vortex model, Divergence-free vector fields in \(\mathbb R^2\), Polynomial mixing under a certain stationary Euler flow, Sobolev regular flows of non-Lipschitz vector fields, Weak solvability of one viscoelastic fractional dynamics model of continuum with memory, Exponential self-similar mixing and loss of regularity for continuity equations, Equivalence of weak solvability of initial-boundary value problems for the Jeffries-Oldroyd model and one integro-differential system with memory, On the weak solvability of a fractional viscoelasticity model, Finite-energy solutions for compressible two-fluid Stokes system, Existence and uniqueness of maximal regular flows for non-smooth vector fields, Improved regularity estimates for Lagrangian flows on \(\mathrm{RCD}(K,N)\) spaces, Weak solvability of a fractional Voigt viscoelasticity model, Singular integrals and a problem on mixing flows, Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and \(\mathrm{RCD}(K,\infty)\) spaces, Solvability of one non-Newtonian fluid dynamics model with memory, Analysis of the implicit upwind finite volume scheme with rough coefficients, A large deviations principle for stochastic flows of viscous fluids, Degenerate SDEs with singular drift and applications to Heisenberg groups, McKean-Vlasov SDEs with drifts discontinuous under Wasserstein distance, Quantitative stability estimates for Fokker-Planck equations, On one problem of viscoelastic fluid dynamics with memory on an infinite time interval, Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients, A unified treatment for ODEs under Osgood and Sobolev type conditions, Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds, On the Sobolev space of functions with derivative of logarithmic order, Distribution dependent SDEs with singular coefficients, The resolution of the Yang-Mills plateau problem in super-critical dimensions, Stochastic flows of SDEs with irregular coefficients and stochastic transport equations, Transport equation: extension of classical results for \(\operatorname{div}b\in\mathrm{BMO}\), Stochastic differential equations with coefficients in Sobolev spaces, Loss of regularity for the continuity equation with non-Lipschitz velocity field, Positive solutions of transport equations and classical nonuniqueness of characteristic curves, Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy, Absolute continuity under flows generated by SDE with measurable drift coefficients, Smooth approximation is not a selection principle for the transport equation with rough vector field, On geometric and analytic mixing scales: comparability and convergence rates for transport problems, Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness, Stochastic Hamiltonian flows with singular coefficients, Two remarks on generalized flows for ordinary differential equations., Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts, On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions, On solvability of a fluid flow alpha-model with memory, Stationary compressible Navier-Stokes equations with inflow condition in domains with piecewise analytical boundaries, Vortex dynamics for 2D Euler flows with unbounded vorticity, Nonuniqueness of weak solutions for the transport equation at critical space regularity, On a priori estimates of weak solutions of one nonhomogeneous problem of dynamics of viscoelastic medium with memory, Derivative estimates on distributions of McKean-Vlasov SDEs, Path-distribution dependent SDEs with singular coefficients, Renormalized solutions to the continuity equation with an integrable damping term, Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations, Lagrangian flows driven by \(BV\) fields in Wiener spaces, Continuity equation and vacuum regions in compressible flows, Regularization by noise in one-dimensional continuity equation, Lipschitz bounds and nonautonomous integrals, Weak solutions for the Stokes system for compressible fluids with general pressure, Convergence of numerical approximations to non-linear continuity equations with rough force fields, Universal mixers in all dimensions, Attractors for model of viscoelastic media with memory motion in non-autonomous case, Support theorem for stochastic differential equations with Sobolev coefficients, A maximal function characterisation of absolutely continuous measures and Sobolev functions, Optimal stability estimates and a new uniqueness result for advection-diffusion equations, New Brezis-van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators, A review of the mean field limits for Vlasov equations, Differentiability in measure of the flow associated with a nearly incompressible BV vector field, Anomalous dissipation in passive scalar transport, Flows of vector fields with point singularities and the vortex-wave system, Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields, Smoothing does not give a selection principle for transport equations with bounded autonomous fields, Logarithmic estimates for continuity equations, Linear transport equations for vector fields with subexponentially integrable divergence
Cites Work
