Browsing Linear and Non-Linear Waves by Title
Now showing items 115-120 of 120
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Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
(2018)The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ... -
Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities
(2018-02-15)We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ... -
Vortex filament equation for a regular polygon
(2014-12-31)In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ... -
Vortex Filament Equation for a regular polygon in the hyperbolic plane
(2020-07-09)The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and ... -
Vortex Filament Equation for some Regular Polygonal Curves
(2020-06-15)One of the most interesting phenomena in fluid literature is the occurrence and evolution of vortex filaments. Some of their examples in the real world are smoke rings, whirlpools, and tornadoes. For an ideal fluid, there ... -
Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations
(2018)We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...