scholarly journals Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum

2021 ◽  
Vol 349 (1) ◽  
pp. 29-41
Author(s):  
Jianjun Xu ◽  
Hongjun Yuan
Keyword(s):  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Initial Energy ◽  
Newtonian Fluids ◽  
Global Strong Solutions

scholarly journals Global Solutions for the Kuramoto-Sivashinsky Equation Posed on Unbounded 3D Grooves

2021 ◽  
pp. 293-303
Author(s):  
N.A. Larkin
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Global Solutions ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Global Strong Solutions ◽  
Initial Boundary Value ◽  
Sivashinsky Equation

Initial boundary value problems for the three-dimensional Kuramoto-Sivashinsky equation posed on unbounded 3D grooves (that may serve as mathematical models for wildfires) were considered. The existence and uniqueness of global strong solutions as well as their exponential decay have been established.

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 Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Representation Formula ◽  
Critical Space ◽  
Lebesgue Spaces ◽  
Initial Value ◽  
Dirac Equations ◽  
Nonlinear Dirac Equations ◽  
Global Strong Solutions ◽  
Solution Representation

We study the initial value problem of some nonlinear Dirac equations which areLmℝcritical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solutionU∈L∞0,T; Ym+2ℝ.

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