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

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 .

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang

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.


1997 ◽  
Vol 127 (6) ◽  
pp. 1193-1205 ◽  
Author(s):  
Feimin Huang

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.


2015 ◽  
Vol 12 (04) ◽  
pp. 787-797 ◽  
Author(s):  
Cleopatra Christoforou

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zujin Zhang

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


2016 ◽  
Vol 26 (04) ◽  
pp. 803-822 ◽  
Author(s):  
Jinkai Li ◽  
Edriss S. Titi ◽  
Zhouping Xin

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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