Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier-Stokes equations: existence and nonuniqueness

DOI10.1214/22-aop1607zbMath1514.35317arXiv2104.09889MaRDI QIDQ6160459

Xiang Chan Zhu, Martina Hofmanová, Rong-Chan Zhu

Publication date: 10 May 2023

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.09889

zbMATH Keywords

stochastic noisenonuniquenessprobabilistically strong solutions3D stochastic Navier-Stokes equationsprobabilistically weak solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) White noise theory (60H40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Weak solutions to PDEs (35D30) Stochastic (Schramm-)Loewner evolution (SLE) (60J67) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

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Cites Work

• Dissipative continuous Euler flows
• Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise
• Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
• On admissibility criteria for weak solutions of the Euler equations
• Ergodicity for the 3D stochastic Navier-Stokes equations
• Invariant measure of scalar first-order conservation laws with stochastic forcing
• The Euler equations as a differential inclusion
• Martingale solutions and Markov selections for stochastic partial differential equations
• A proof of Onsager's conjecture
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Semiflow selection for the compressible Navier-Stokes system
• Semiflow selection and Markov selection theorems
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• Global well-posedness of the 3D Navier-Stokes equations perturbed by a deterministic vector field
• Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent
• Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
• Non-uniqueness in law for the Boussinesq system forced by random noise
• Sharp nonuniqueness for the Navier-Stokes equations
• Dissipative solutions and semiflow selection for the complete Euler system
• Convex integration and phenomenologies in turbulence
• Markov selection for the stochastic compressible Navier-Stokes system
• Non uniqueness of power-law flows
• Solution semiflow to the isentropic Euler system
• On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
• Anomalous dissipation for \(1/5\)-Hölder Euler flows
• The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities
• Markov selections for the 3D stochastic Navier-Stokes equations
• Three-dimensional Navier-Stokes equations driven by space-time white noise
• PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
• An Introduction to 3D Stochastic Fluid Dynamics
• Onsager's Conjecture for Admissible Weak Solutions
• ON THE SELECTION OF A MARKOV PROCESS FROM A SYSTEM OF PROCESSES AND THE CONSTRUCTION OF QUASI-DIFFUSION PROCESSES
• On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations
• NonUniqueness in Law for Two-Dimensional Navier--Stokes Equations with Diffusion Weaker than a Full Laplacian
• Convex integration constructions in hydrodynamics
• Ill posedness for the full Euler system driven by multiplicative white noise
• On Ill‐ and <scp>Well‐Posedness</scp> of Dissipative Martingale Solutions to Stochastic <scp>3D</scp> Euler Equations
• Stochastic Equations in Infinite Dimensions

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