University of Sussex
Browse

Topology of twists, extremising twist paths and multiple solutions to the nonlinear system in variation L [u] = ?P

Download (447.98 kB)
journal contribution
posted on 2023-06-09, 17:38 authored by George Morrison, Ali TaheriAli Taheri
In this paper we address questions on the existence and multiplicity of a class of geometrically motivated mappings with certain symmetries that serve as solutions to the nonlinear system in variation: [equation not shown] Here ? ? R n is a bounded domain, F = F(r, s, ?) is a sufficiently smooth Lagrangian, Fs = Fs(|x|, |u| 2 , |?u| 2 ) and F? = F?(|x|, |u| 2 , |?u| 2 ) with Fs and F? denoting the derivatives of F with respect to the second and third variables respectively while P is an a priori unknown hydrostatic pressure resulting from the incompressibility constraint det ?u = 1. Among other things, by considering twist mappings u with an SO(n)-valued twist path, we prove the existence of multiple and topologically distinct solutions to ELS for n = 2 even versus the only (non) twisting solution u = x for n = 3 odd. An extremality analysis for twist paths and those of Lie exponential types and a suitable formulation of a differential operator action on twists relating to ELS are the key ingredients in the proof.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Topological Methods in Nonlinear Analysis

ISSN

1230-3429

Publisher

Juliusz Schauder Center for Nonlinear Studies

Issue

2A

Volume

54

Page range

833-862

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-04-26

First Open Access (FOA) Date

2020-11-10

First Compliant Deposit (FCD) Date

2019-04-26

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC