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13 papers · 2 filters
Wrinkling of a thin circular sheet bonded to a spherical substrate
Peter Bella, Robert V. Kohn
We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding…
Defects of liquid crystals with variable degree of orientation
Onur Alper, Robert Hardt, Fang-Hua Lin
We prove that the zero set of a minimizer of the modified Ericksen energy for nematic liquid crystals with variable degree of orientation consists locally of isolated points and a…
Regularity for Shape Optimizers: The Nondegenerate Case
Dennis Kriventsov, Fanghua Lin
We consider minimizers of \[ F(λ_1(Ω),\ldots,λ_N(Ω)) + |Ω|, \] where is a function strictly increasing in each parameter, and is the -th Dirichlet eigenvalue of …
Gevrey Stability of Prandtl Expansions for 2D Navier-Stokes
David Gerard-Varet, Yasunori Maekawa, Nader Masmoudi
We investigate the stability of boundary layer solutions of the two-dimensional incompressible Navier-Stokes equations. We consider shear flow solutions of Prandtl type : $$ u^ν(t,…
Finite depth gravity water waves in holomorphic coordinates
Benjamin Harrop-Griffiths, Mihaela Ifrim, Daniel Tataru
In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the…
Quantitative analysis of boundary layers in periodic homogenization
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat +1
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estim…