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5 papers · 2 filters
Homotopies of Eigenfunctions and the Spectrum of the Laplacian on the Sierpinski Carpet
Steven M. Heilman, Robert S. Strichartz
Consider a family of bounded domains in the plane (or more generally any Euclidean space) that depend analytically on the parameter , and consider the ordinary Neumann L…
Remarks on the Blowup Criteria for Oldroyd Models
Zhen Lei, Nader Masmoudi, Yi Zhou
We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in \cite{CM} in two space dimensions. Our method is much easier…
Global Solutions for the Gravity Water Waves Equation in Dimension 3
P. Germain, N. Masmoudi, J. Shatah
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^…
Well and ill-posedness issues for energy supercritical waves
Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi
We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. We also obta…
Outer Approximation of the Spectrum of a Fractal Laplacian
Tyrus Berry, Steven M. Heilman, Robert S. Strichartz
We present a new method to approximate the Neumann spectrum of a Laplacian on a fractal K in the plane as a renormalized limit of the Neumann spectra of the standard Laplacian on a…