Cover Image

The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	An, Xinliang, Chen, Haoyang, Yin, Silu
Format:	Preprint
Published:	2022
Subjects:	Analysis of PDEs Mathematical Physics Fluid Dynamics
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Low regularity ill-posedness and shock formation for 3D ideal compressible MHD
by: An, Xinliang, et al.
Published: (2021)

Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$
by: Chen, Jiajie
Published: (2024)

Vorticity blowup in 2D compressible Euler equations
by: Chen, Jiajie, et al.
Published: (2024)

A Hamiltonian Dysthe equation for hydroelastic waves in a compressed ice sheet
by: Guyenne, Philippe, et al.
Published: (2024)

On the removal of the barotropic condition in helicity studies of the compressible Euler and ideal compressible MHD equations
by: Boutros, Daniel W., et al.
Published: (2025)

Infinite norm of the derivative of the solution operator of Euler equations
by: Li, Y. Charles
Published: (2020)

Inertial Momentum Dissipation for Viscosity Solutions of Euler Equations: External Flow Around a Smooth Body
by: Quan, Hao, et al.
Published: (2022)

Solitary wave formation in the compressible Euler equations
by: Ketcheson, David I., et al.
Published: (2024)

Variational structure and two-dimensional subsonic jet flows for compressible Euler system with general incoming flows
by: Li, Yan, et al.
Published: (2020)

Amplitude blowup in compressible Euler flows without shock formation
by: Jenssen, Helge Kristian
Published: (2025)

Space-Time Statistical Solutions of the Incompressible Euler Equations and Landau-Lifshitz Fluctuating Hydrodynamics
by: Eyink, Gregory L., et al.
Published: (2024)

Robust series linearization of nonlinear advection-diffusion equations
by: Kieffer, T. Forrest, et al.
Published: (2025)

Bilayer one-dimensional Convection-Diffusion-Reaction-Source problem. Analytical and numerical solution
by: Umbricht, Guillermo Federico, et al.
Published: (2024)

Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density in a finite channel
by: Zhao, Weiren
Published: (2023)

Phase-Textured Complex Viscosity in Linear Viscous Flows: Non-Normality Without Advection, Corner Defects, and 3D Mode Coupling
by: Kleess, Lillian St.
Published: (2026)

The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions
by: Shkoller, Steve, et al.
Published: (2023)

Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity
by: Doak, Alex, et al.
Published: (2025)

On global existence and large-time behaviour of weak solutions to the compressible barotropic Navier--Stokes Equations on $\mathbb{T}^2$ with density-dependent bulk viscosity: beyond the Va\uıgant--Kazhikhov regime
by: Li, Siran, et al.
Published: (2024)

Shock Formation for Compressible Euler Equations on $\mathbb{S}^2$
by: An, Xinliang, et al.
Published: (2025)

Estimates for the 2D Navier-Stokes equations: the effects of forcing
by: Mukherjee, Ritwik, et al.
Published: (2025)

Dissipation concentration in two-dimensional fluids
by: De Rosa, Luigi, et al.
Published: (2025)

On higher-order derivative ratios in turbulent flows
by: Grujić, Zoran, et al.
Published: (2026)

Mathematical Theorems on Turbulence
by: Drivas, Theodore D.
Published: (2026)

Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas
by: Armstrong, Scott, et al.
Published: (2025)

Compressible N-phase fluid mixture models
by: Eikelder, M. F. P. ten, et al.
Published: (2025)

Asymptotic models for viscoelastic one-dimensional blood flow
by: Alonso-Orán, Diego, et al.
Published: (2026)

Weakly nonlinear models for hydroelastic water waves
by: Alonso-Orán, Diego, et al.
Published: (2026)

Intermittency and Dissipation Regularity in Turbulence
by: De Rosa, Luigi, et al.
Published: (2025)

Quantitative enstrophy bounds for measure vorticities
by: De Rosa, Luigi, et al.
Published: (2026)

A Proof of Onsager's Conjecture
by: Isett, Philip
Published: (2016)

Singular vortex pairs follow magnetic geodesics
by: Drivas, Theodore D., et al.
Published: (2024)

On the Mathematical Analysis and Physical Implications of the Principle of Minimum Pressure Gradient
by: Taha, Haithem
Published: (2026)

Derivation and well-posedness for asymptotic models of cold plasmas
by: Alonso-Orán, Diego, et al.
Published: (2023)

Quantum-Inspired Stochastic Modeling and Regularity in Turbulent Fluid Dynamics
by: Santos, Rômulo Damasclin Chaves dos, et al.
Published: (2024)

Traveling gravity-capillary waves with odd viscosity
by: Alonso-Orán, Diego, et al.
Published: (2024)

Forward self-similar solutions to the 2D Navier--Stokes equations
by: Albritton, Dallas, et al.
Published: (2026)

Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
by: Wang, Zhi-Wei, et al.
Published: (2026)

Multi-Sink Solutions to the Self-Similar Euler Equations
by: Choi, Hyungjun, et al.
Published: (2026)

Evaluating Joule heating influence on heat transfer and entropy generation in MHD channel flow: A parametric study and ill-posed problem solution using PINNs
by: Ghaderi, Ehsan, et al.
Published: (2024)

A thermodynamics-based turbulence model for isothermal compressible flows
by: Ma, Zhiting, et al.
Published: (2025)