# Collapse Versus Blow-Up and Global Existence in the Generalized Constantin-Lax-Majda Equation

@article{Lushnikov2021CollapseVB,
title={Collapse Versus Blow-Up and Global Existence in the Generalized Constantin-Lax-Majda Equation},
author={Pavel M. Lushnikov and Denis A. Silantyev and Michael Siegel},
journal={J. Nonlinear Sci.},
year={2021},
volume={31},
pages={82}
}
• Published 2 October 2020
• Mathematics
• J. Nonlinear Sci.
The question of finite time singularity formation vs. global existence for solutions to the generalized Constantin-Lax-Majda equation is studied, with particular emphasis on the influence of a parameter $a$ which controls the strength of advection. For solutions on the infinite domain we find a new critical value $a_c=0.6890665337007457\ldots$ below which there is finite time singularity formation % if we write a=a_c=0.6890665337007457\ldots here then \ldots doesn't fit into the line that has a…

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