3 problems

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Majda's conjecture on finite-time regularity of weakly nonlinear systems
Majda's conjecture. Smooth initial data for weakly nonlinear systems do not break in finite time. This conjecture concerns finite-time breakdown and global smoothness for linearly…
Conjectureopenhyperbolic-pdes integrable-systems quasilinear-systemsarXiv posted 2 days ago
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No finite-time gradient catastrophe for generic solutions of the system
Let the system referred to as … for generic initial data do not develop a point of gradient catastrophe in finite time. The source presents this as a task for investigation in nume…
Conjectureopengradient-catastrophe integrable-systems quasilinear-systemsarXiv posted 2 days ago
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Linear degeneracy conjecture for higher-dimensional integrable quasilinear systems
Let an $n$ -component $(d+1)$ -dimensional integrable quasilinear system be given, with $d\geq 3$ , and suppose that its dispersion relation is irreducible. A system is linearly degen…
Conjectureopenintegrable-systems linear-degeneracy quasilinear-systemsarXiv posted 2 days ago

Majda's conjecture on finite-time regularity of weakly nonlinear systems