Finite-time singularities in surface-diffusion instabilities are cured by plasticity

Finite-time singularities in surface-diffusion instabilities are cured by plasticity.

A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite...

Classification of possible finite-time singularities by functional renormalization.

Starting from a representation of the early time evolution of a dynamical system in terms of the polynomial expression of some observable phi(t) as a function of the time variable in some interval 0 < or = t < or = T, we investigate how to extrapolate/forecast in some optimal stability sense the future evolution of phi(t) for time t>T. Using the functional renormalization of Yukalov and Gluzman...

Finite Time Singularities for Hyperbolic Systems

In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the variational wave equations as those in [18]. The system posses a unique C solution before the emergence of vacuum in finite time, for given initial data that are smooth enough, bounded and uniformly away from vacuum. At...

Finite-time Euler singularities: A Lagrangian perspective

Finite Time Singularities for a Class of Generalized Surface Quasi-geostrophic Equations

We propose and study a class of generalized surface quasi-geostrophic equations. We show that in the inviscid case certain radial solutions develop gradient blow-up in finite time. In the critical dissipative case, the equations are globally well-posed with arbitrary H1 initial data.