Ill-posedness for the Euler equations in Besov spaces

DOI10.1016/j.nonrwa.2023.103941zbMath1529.35358arXiv2104.06408OpenAlexW4381547472MaRDI QIDQ6171340

Weipeng Zhu, Yanghai Yu, Jinlu Li

Publication date: 11 August 2023

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.06408

zbMATH Keywords

Euler equationsBesov spacesill-posedness

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Non-uniform dependence on initial data for the CH equation on the line.
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• Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics
• On nonstationary flows of viscous and ideal fluids in \(L^ p_ s({\mathbb{R}}^ 2)\)
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Local well-posedness of the incompressible Euler equations in \(B_{\infty, 1}^1\) and the inviscid limit of the Navier-Stokes equations
• Non-uniform dependence for Euler equations in Besov spaces
• Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces
• Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces
• Local ill-posedness of the incompressible Euler equations in \(C^1\) and \(B^1_{\infty,1}\)
• Fourier Analysis and Nonlinear Partial Differential Equations
• Existence of Solution for the Euler Equations in a Critical Besov Space (ℝⁿ)
• Ill-posedness of the basic equations of fluid dynamics in Besov spaces
• Non-Uniform Dependence for the Periodic CH Equation
• Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces

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