Singularity formation for a fluid mechanics model with nonlocal velocity

DOI10.4310/CMS.2019.v17.n7.a2zbMath1433.35298arXiv1708.09360WikidataQ126406282 ScholiaQ126406282MaRDI QIDQ2285631

Changhui Tan

Publication date: 8 January 2020

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09360

zbMATH Keywords

singularity formationquasi-geostrophic equationsporous medium flowEuler alignment equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Meteorology and atmospheric physics (86A10) Fractional partial differential equations (35R11) PDEs in connection with geophysics (35Q86)

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Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system ⋮ Global Existence and Limiting Behavior of Unidirectional Flocks for the Fractional Euler Alignment System ⋮ Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment ⋮ Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment ⋮ Global solutions to the tangential Peskin problem in 2-D ⋮ Finite- and infinite-time cluster formation for alignment dynamics on the real line ⋮ Local well-posedness of the topological Euler alignment models of collective behavior ⋮ Topologically Based Fractional Diffusion and Emergent Dynamics with Short-Range Interactions ⋮ Singularity formation for the fractional Euler-alignment system in 1D ⋮ Global well-posedness for the Euler alignment system with mildly singular interactions ⋮ On Cucker–Smale dynamical systems with degenerate communication ⋮ Global regularity for a 1D Euler-alignment system with misalignment ⋮ Flocking with short-range interactions

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