On a one-dimensional 𝛼-patch model with nonlocal drift and fractional dissipation

DOI10.1090/S0002-9947-2013-06075-8zbMath1302.35334arXiv1207.0957MaRDI QIDQ5401752

Hongjie Dong, Dong Li

Publication date: 12 March 2014

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

Full work available at URL: https://arxiv.org/abs/1207.0957

zbMATH Keywords

one-dimensionallarge initial datanonlocal nonlinear equationfractional dissipation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)

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Cites Work

• Nonlocal maximum principles for active scalars
• Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations
• Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation
• Global well-posedness of the critical Burgers equation in critical Besov spaces
• Blow up and regularity for fractal Burgers equation
• Integral inequalities for the Hilbert transform applied to a nonlocal transport equation
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
• Well-posedness for a transport equation with nonlocal velocity
• Regularity of solutions for the critical \(N\)-dimensional Burgers' equation
• Fractal Burgers equations
• A maximum principle applied to quasi-geostrophic equations
• Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation
• Existence for the \(\alpha \)-patch model and the QG sharp front in Sobolev spaces
• Formation of singularities for a transport equation with nonlocal velocity
• Singularity formations for a surface wave model
• OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS
• Finite time singularities for a class of generalized surface quasi-geostrophic equations
• On a generalization of the Constantin–Lax–Majda equation
• Finite time singularities and global well-posedness for fractal Burgers equations
• Evidence of singularities for a family of contour dynamics equations

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