scholarly journals Global existence and scattering for quadratic NLS with potential in three dimensions

2021 ◽  
Vol 14 (7) ◽  
pp. 1977-2046
Author(s):  
Tristan Léger
Keyword(s):  
Global Existence ◽  
Three Dimensions

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

scholarly journals Cahn–Hilliard equations incorporating elasticity: analysis and comparison to experiments

2013 ◽  
Vol 371 (2005) ◽  
pp. 20120342 ◽  
Author(s):  
Thomas Blesgen ◽  
Isaac Vikram Chenchiah
Keyword(s):  
Energy Density ◽  
Global Existence ◽  
Three Dimensions ◽  
Elasticity Analysis ◽  
Micro Structure ◽  
Existence Of Weak Solutions ◽  
Hilliard Equation ◽  
Elastic Energy Density ◽  
Theoretical Predictions ◽  
Cahn Hilliard Equation

We consider a generalization of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasi-convex, incorporates micro-structure formation on smaller length scales. We explore the global existence of weak solutions in two and three dimensions. We compare theoretical predictions with experimental observations of coarsening in superalloys.

scholarly journals On a Bingham fluid whose viscosity and yield limit depend on the temperature

1992 ◽  
Vol 128 ◽  
pp. 1-14 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Initial Velocity ◽  
Local Existence ◽  
Strong Solutions ◽  
Bingham Fluid ◽  
Affirmative Answer ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Yield Limit

Duvaut and Lions [2] studied the field of velocities and of temperatures in a moving incompressible Bingham fluid endowed with viscosity μ(θ) depending on the temperature θ and established the existence of a weak solution in the case of a two dimensional fluid. However, the problem of uniqueness remained unsolved. The purpose of the present paper is to give an affirmative answer to the problem, that is, to show the local existence (resp. the global existence) in the time and the uniqueness of (strong) solutions in three dimensions under the conditions that (i) the time (resp. the initial velocity and the external force) and (ii) the rate of variation of the viscosity and the yield limit with respect to the temperature are both sufficiently small. It will be easily seen that the global existence and the uniqueness also hold in the two dimensional case whenever the rate (ii) is sufficiently small.

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

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