Local well-posedness for the quasi-geostrophic equations in Besov-Lorentz spaces

DOI10.1007/s12215-018-0388-0zbMath1439.35483OpenAlexW2906195728MaRDI QIDQ2174813

Yehua Zhang, Qian Zhang

Publication date: 27 April 2020

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-018-0388-0

zbMATH Keywords

local well-posednessblow-up criterionquasi-geostrophic equationsBesov-Lorentz spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Hydrology, hydrography, oceanography (86A05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlocal maximum principles for active scalars
• Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
• On the well-posedness of the quasi-geostrophic equation in the Triebel-Lizorkin-Lorentz spaces
• On the well-posedness of the ideal MHD equations in the Triebel-Lizorkin spaces
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Eventual regularization for the slightly supercritical quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces
• Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
• Local well-posedness for the 2D non-dissipative quasi-geostrophic equation in Besov spaces
• Global well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces
• Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Vorticity and Incompressible Flow
• Incompressible flow in porous media with fractional diffusion
• Dissipative Quasi-Geostrophic Equation: Local Well-posedness, Global Regularity and Similarity Solutions
• Classical Fourier Analysis
• On the Global Well-Posedness of the Critical Quasi-Geostrophic Equation
• Quasi-geostrophic-type equations with initial data in Morrey spaces
• Inviscid limits and regularity estimates for the solutions of the 2-D dissipative quasi-geostrophic equations
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• The quasi-geostrophic equation in the Triebel Lizorkin spaces
• The two-dimensional quasi-geostrophic equation with critical or supercritical dissipation
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Scalars convected by a two-dimensional incompressible flow
• On the well‐posedness of the Euler equations in the Triebel‐Lizorkin spaces
• Singular front formation in a model for quasigeostrophic flow
• Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow