On the Behaviors of Solutions Near Possible Blow-Up Time in the Incompressible Euler and Related Equations |
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Authors: | Dongho Chae |
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Institution: | 1. Department of Mathematics , Sungkyunkwan University , Suwon, Korea chae@skku.edu |
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Abstract: | We study behaviors of scalar quantities near the possible blow-up time, which is made of smooth solutions of the Euler equations, Navier–Stokes equations and the surface quasi-geostrophic equations. Integrating the dynamical equations of the scaling invariant norms, we derive the possible blow-up behaviors of the above quantities, from which we obtain new type of blow-up criteria and some necessary conditions for the finite time blow-up. |
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Keywords: | Euler equations Finite time blow-up Navier–Stokes equations Quasi-geostrophic equations |
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