Sommerfeld Paradox - A Novel Study (2009)
Lan, Yueheng, Li, Y. Charles, Lin, Zhiwu
Sommerfeld paradox roughly says that mathematically Couette shear flow is linearly stable for all Reynolds number, but experimentally it is unstable to any size perturbation when the Reynolds number...
A Resolution of the Sommerfeld Paradox (2009)
Sommerfeld paradox roughly says that mathematically Couette linear shear is linearly stable for all Reynolds number, but experimentally arbitrarily small perturbations can induce the transition from...
On Linear Instability of 2D Solitary Water Waves (2009)
We consider instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are known to not be attained at the highest wave that has a 120 angle at...
Instability of large solitary water waves (2008)
We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120...
Instability of nonlinear dispersive solitary waves (2008)
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive...
Stability of peakons for the Degasperis-Procesi equation (2007)
The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the...
Unstable surface waves in running water (2007)
Hur, Vera Mikyoung, Lin, Zhiwu
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion...
Unstable and Stable Galaxy Models (2007)
To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability...
A sharp stability criterion for the Vlasov-Maxwell system (2007)
We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose...
Nonlinear instability of ideal plane flows (2004)
We study nonlinear instability of stationary ideal plane flows. For any bounded domain and very general steady flows, we show that if the linearized equation has an exponentially growing solution,...
Stability and instability of equilibria in collisionless plasmas and ideal plane flows / (2003)
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