On the singularity problem for the Euler equations

DOI10.1007/978-981-19-3708-8_2zbMath1499.35001OpenAlexW4312849345MaRDI QIDQ2104785

Publication date: 7 December 2022

Full work available at URL: https://doi.org/10.1007/978-981-19-3708-8_2

PDEs in connection with fluid mechanics (35Q35) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics (76-01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations (35-01) Blow-up in context of PDEs (35B44) Euler equations (35Q31)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
On formation of a locally self-similar collapse in the incompressible Euler equations
On the well-posedness of the ideal MHD equations in the Triebel-Lizorkin spaces
On the generalized self-similar singularities for the Euler and the Navier-Stokes equations
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
Bilinear estimates in \(BMO\) and the Navier-Stokes equations
Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation
On the local type I conditions for the 3D Euler equations
Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary
Remarks on type I blow-up for the 3D Euler equations and the 2D Boussinesq equations
Localized non blow-up criterion of the Beale-Kato-Majda type for the 3D Euler equations
Energy concentrations and type I blow-up for the 3D Euler equations
The Euler equations in a critical case of the generalized Campanato space
Euler's equations and the maximum principle
Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations
Removing type II singularities off the axis for the three dimensional axisymmetric Euler equations
Nonexistence of self-similar singularities for the 3D incompressible Euler equations
On the regularity of solutions to the 2D Boussinesq equations satisfying type I conditions
Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations
Global regularity for the 2D Boussinesq equations with partial viscosity terms
Unique continuation type theorem for the self-similar Euler equations
Nonstationary flows of viscous and ideal fluids in \(R^3\)
Finite-time singularity formation for strong solutions to the Boussinesq system
Vorticity and Incompressible Flow
On functions of bounded mean oscillation
On the finite-time singularities of the 3D incompressible Euler equations
Euler equations for incompressible ideal fluids
Commutator estimates and the euler and navier-stokes equations
Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
Evidence for a singularity of the three-dimensional, incompressible Euler equations
Geometric Statistics in Turbulence
Local existence and blow-up criterion for the Boussinesq equations
On Squirt Singularities in Hydrodynamics
Some Remarks on Topological Fluid Mechanics
On the well‐posedness of the Euler equations in the Triebel‐Lizorkin spaces
Geometric constraints on potentially
A study of energy concentration and drain in incompressible fluids
On a Type I Singularity Condition in Terms of the Pressure for the Euler Equations in ℝ3
Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study
Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation
Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation
On the Euler equations of incompressible fluids
Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
Localized blow-up criterion for \(C^{1, \alpha}\) solutions to the 3D incompressible Euler equations

This page was built for publication: On the singularity problem for the Euler equations