On Le Jan-Sznitman's stochastic approach to the Navier-Stokes equations

DOI10.1090/tran/8974zbMATH Open1543.35134MaRDI QIDQ6567140

Enrique A. Thomann, Radu Dascaliuc, T. N. Pham

Publication date: 4 July 2024

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Navier-Stokes equationsHerz spacesFourier-Besov spacesstochastic cascadesminimal blow-up data

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces
• Minimal initial data for potential Navier-Stokes singularities
• The Navier-Stokes equations and weak Herz spaces
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Stochastic cascades and 3-dimensional Navier-Stokes equations
• Smooth or singular solutions to the Navier-Stokes system?
• Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces
• Doubly stochastic Yule cascades. I: The explosion problem in the time-reversible case
• The well-posedness of the incompressible magnetohydrodynamic equations in the framework of Fourier-Herz space
• A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion
• On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• On the movement of a space-filling viscous liquid
• Stochastic explosion and non-uniqueness for \(\alpha\)-Riccati equation
• Finite time blow up for a Navier-Stokes like equation
• Exponent bounds for a convolution inequality in Euclidean space with applications to the Navier-Stokes equations
• Fourier Analysis and Nonlinear Partial Differential Equations
• Stochastic Processes with Applications
• Stochastic solutions of some nonlinear partial differential equations
• The Navier-Stokes Problem in the 21st Century
• Zeros of complex caloric functions and singularities of complex viscous Burgers equation
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations
• About the behavior of regular Navier-Stokes solutions near the blow up
• Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
• Global mild solutions of Navier‐Stokes equations
• Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS
• Well-posedness for the Navier-Stokes equations

This page was built for publication: On Le Jan-Sznitman's stochastic approach to the Navier-Stokes equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6567140)