scholarly journals The Cauchy Problem for the Incompressible 2D-MHD with Power Law-Type Nonlinear Viscous Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Power Law ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Fluid Flows ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We investigate a motion of the incompressible 2D-MHD with power law-type nonlinear viscous fluid. In this paper, we establish the global existence and uniqueness of a weak solution u , b depending on a number q in ℝ 2 . Moreover, the energy norm of the weak solutions to the fluid flows has decay rate 1 + t − 1 / 2 .

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 Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Energy Conservation ◽  
Classical Solution ◽  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

Existence and uniqueness of discontinuous solutions for a hyperbolic system

1997 ◽  
Vol 127 (6) ◽  
pp. 1193-1205 ◽  
Author(s):  
Feimin Huang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Hyperbolic System ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Discontinuous Solutions ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

In this paper, we prove the global existence and uniqueness of solutions to the Cauchy problem of a hyperbolic system, which probably contains so-called δ-waves.

scholarly journals A remark on the Glimm scheme for inhomogeneous hyperbolic systems of balance laws

2015 ◽  
Vol 12 (04) ◽  
pp. 787-797 ◽  
Author(s):  
Cleopatra Christoforou
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Weak Solutions ◽  
State Vector ◽  
Equilibrium Solution ◽  
Hyperbolic Systems ◽  
Balance Laws ◽  
Glimm Scheme ◽  
Systems Of Balance Laws ◽  
The Cauchy Problem

General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small BV data under appropriate assumptions on the decay of the flux and the source with respect to space and time. There is neither a hypothesis about equilibrium solution nor about the dependence of the source on the state vector as previous results have assumed.

scholarly journals Global Regularity for the 2D Micropolar Fluid Flows with Mixed Partial Dissipation and Angular Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zujin Zhang
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Global Regularity ◽  
Fluid Flows ◽  
Classical Solutions ◽  
Partial Dissipation ◽  
Global Existence And Uniqueness

This paper establishes the global existence and uniqueness of classical solutions to the 2D micropolar fluid flows with mixed partial dissipation and angular viscosity.

scholarly journals On the uniqueness of weak solutions to the Ericksen–Leslie liquid crystal model in ℝ2

2016 ◽  
Vol 26 (04) ◽  
pp. 803-822 ◽  
Author(s):  
Jinkai Li ◽  
Edriss S. Titi ◽  
Zhouping Xin
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Liquid Crystal ◽  
Weak Solutions ◽  
Energy Estimates ◽  
Unique Weak Solution ◽  
The Cauchy Problem ◽  
Crystal Model ◽  
Main Ideas ◽  
Leslie System

This paper concerns the uniqueness of weak solutions to the Cauchy problem to the Ericksen–Leslie system of liquid crystal models in [Formula: see text], with both general Leslie stress tensors and general Oseen–Frank density. It is shown here that such a system admits a unique weak solution provided that the Frank coefficients are close to some positive constant. One of the main ideas of our proof is to perform suitable energy estimates at the level one order lower than the natural basic energy estimates for the Ericksen–Leslie system.

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