scholarly journals Global Well-Posedness of Incompressible Elastodynamics in Two Dimensions

2016 ◽  
Vol 69 (11) ◽  
pp. 2072-2106 ◽  
Author(s):  
Zhen Lei
Keyword(s):  
Two Dimensions ◽  
Well Posedness

Global well-posedness for the averaged Euler equations in two dimensions

2000 ◽  
Vol 138 (3-4) ◽  
pp. 197-209 ◽  
Author(s):  
Shinar Kouranbaeva ◽  
Marcel Oliver
Keyword(s):  
Euler Equations ◽  
Two Dimensions ◽  
Well Posedness

WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN–SIMONS–DIRAC SYSTEM IN TWO DIMENSIONS

2013 ◽  
Vol 10 (04) ◽  
pp. 735-771 ◽  
Author(s):  
MAMORU OKAMOTO
Keyword(s):  
Cauchy Problem ◽  
Dirac Equation ◽  
Sobolev Space ◽  
Gauge Invariance ◽  
Two Dimensions ◽  
Well Posedness ◽  
Dirac System ◽  
The Cauchy Problem ◽  
Chern Simons ◽  
Well Posed

We consider the Cauchy problem associated with the Chern–Simons–Dirac system in ℝ1+2. Using gauge invariance, we reduce the Chern–Simons–Dirac system to a Dirac equation and we uncover the null structure of this Dirac equation. Next, relying on null structure estimates, we establish that the Cauchy problem associated with this Dirac equation is locally-in-time well-posed in the Sobolev space Hs for all s > 1/4. Our proof uses modified L4-type estimates.

scholarly journals Well-Posedness of Strong Solutions to the Anelastic Equations of Stratified Viscous Flows

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Xin Liu ◽  
Edriss S. Titi
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Physical Vacuum ◽  
Well Posedness ◽  
Small Initial Data ◽  
Anelastic Equations

Abstract We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken into account, and the density background profile is permitted to have physical vacuum singularity. The existing time of the solutions is infinite in two dimensions, with general initial data, and in three dimensions with small initial data.

scholarly journals On the well-posedness of the stochastic Allen–Cahn equation in two dimensions

2012 ◽  
Vol 231 (6) ◽  
pp. 2537-2550 ◽  
Author(s):  
Marc D. Ryser ◽  
Nilima Nigam ◽  
Paul F. Tupper
Keyword(s):  
Two Dimensions ◽  
Well Posedness ◽  
Cahn Equation

scholarly journals Thermodynamically consistent Navier–Stokes–Cahn–Hilliard models with mass transfer and chemotaxis

2017 ◽  
Vol 29 (4) ◽  
pp. 595-644 ◽  
Author(s):  
KEI FONG LAM ◽  
HAO WU
Keyword(s):  
Mass Transfer ◽  
Chemical Potential ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Well Posedness ◽  
Global Weak Solutions ◽  
Two Phase ◽  
Model Variant

We derive a class of Navier–Stokes–Cahn–Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier–Stokes analogues of earlier Cahn–Hilliard–Darcy models proposed for modelling tumour growth, and are derived based on a volume-averaged velocity, which yields simpler expressions compared to models derived based on a mass-averaged velocity. Then, we perform mathematical analysis on a simplified model variant with zero excess of total mass and equal densities. We establish the existence of global weak solutions in two and three dimensions for prescribed mass transfer terms. Under additional assumptions, we prove the global strong well-posedness in two dimensions with variable fluid viscosity and mobilities, which also includes a continuous dependence on initial data and mass transfer terms for the chemical potential and the order parameter in strong norms.

scholarly journals Dynamic cubic instability in a 2D Q-tensor model for liquid crystals

2015 ◽  
Vol 25 (08) ◽  
pp. 1477-1517 ◽  
Author(s):  
Gautam Iyer ◽  
Xiang Xu ◽  
Arghir D. Zarnescu
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Initial Data ◽  
Elastic Constant ◽  
Nematic Liquid Crystal ◽  
Gradient Flow ◽  
Two Dimensions ◽  
Tensor Model ◽  
Well Posedness

We consider a four-elastic-constant Landau–de Gennes energy characterizing nematic liquid crystal configurations described using the Q-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering an L2 gradient flow generated by this energy. We work in two dimensions and concentrate on understanding the relations between the physicality of the initial data and the global well-posedness of the system.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

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