Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations.

Gliklikh, Yuri E.; Morozova, Lora A.

Displaying similar documents to “Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations.”

Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.

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On the $L^{2}$ -instability and $L^{2}$ -controllability of steady flows of an ideal incompressible fluid

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In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in $L^{2}$ vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...

On the $L^{2}$ -instability of fluid flows

Alexander Shnirelman (1999-2000)

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A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds

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We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time...

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