75 research outputs found
On the large-distance asymptotics of steady state solutions of the Navier–Stokes equations in 3D exterior domains
Diffeomorphic approximation of Sobolev homeomorphisms
Every homeomorphism h : X -> Y between planar open sets that belongs to the
Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm
by diffeomorphisms.Comment: 21 pages, 5 figure
On derivation of Euler-Lagrange Equations for incompressible energy-minimizers
We prove that any distribution satisfying the equation for some tensor () -the
{\it local Hardy space}, is in , and is locally represented by the sum
of singular integrals of with Calder\'on-Zygmund kernel. As a
consequence, we prove the existence and the local representation of the
hydrostatic pressure (modulo constant) associated with incompressible
elastic energy-minimizing deformation satisfying . We also derive the system of Euler-Lagrange
equations for incompressible local minimizers that are in the space
; partially resolving a long standing problem. For H\"older
continuous pressure , we obtain partial regularity of area-preserving
minimizers.Comment: 23 page
The masterpieces of John Forbes Nash Jr.
In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader
A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation
Liquid crystals and their defects
These lecture notes discuss classical models of liquid crystals, and the
different ways in which defects are described according to the different
models.Comment: CIME lecture course, Cetraro, 201
On global weak solutions to the Cauchy problem for the Navier-Stokes equations with large L3-initial data
The aim of the note is to discuss different definitions of solutions to the Cauchy problem for the Navier-Stokes equations with the initial data belonging to the Lebesgue space L3(R3
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