scholarly journals Global strong solutions of equations of magnetohydrodynamic type

1997 ◽  
Vol 38 (3) ◽  
pp. 291-306 ◽  
Author(s):  
Marko A. Rojas-Medar ◽  
José Luiz Boldrini
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Error Bounds ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
System Of Equations ◽  
Spectral Galerkin Method ◽  
Global Strong Solutions ◽  
Solutions Of Equations

AbstractBy using the spectral Galerkin method, we prove a result on the global existence in time of strong solutions for a system of equations of magnetohydrodynamic type. Several estimates for the solution and their approximations are given. These estimates can be used in the derivation of error bounds for the approximate solutions.

scholarly journals Magneto-micropolar fluid motion: global existence of strong solutions

1999 ◽  
Vol 4 (2) ◽  
pp. 109-125 ◽  
Author(s):  
Elva E. Ortega-Torres ◽  
Marko A. Rojas-Medar
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Error Bounds ◽  
Micropolar Fluid ◽  
Fluid Motion ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Time Estimates ◽  
Spectral Galerkin Method ◽  
External Forces

By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of magneto-micropolar fluid without assuming that the external forces decay with time. We also derive uniform in time estimates of the solution that are useful for obtaining error bounds for the approximate solutions.

Solutions with Singular Initial Data for a Model of Electrophoretic Separation

1990 ◽  
Vol 33 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Joel D. Avrin
Keyword(s):  
Initial Data ◽  
Diffusion Coefficients ◽  
Existence Result ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Electrophoretic Separation ◽  
Small Diffusion ◽  
Singular Initial Data ◽  
Global Strong Solutions ◽  
Global Existence Result

AbstractUnique global strong solutions of a Cauchy problem arising in electrophoretic separation are constructed with arbitrary initial data in L1, thus generalizing an earlier global existence result. For small diffusion coefficients, the solutions can be viewed as approximate solutions for the corresponding zero-diffusion Riemann problem.

scholarly journals Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Boyan Jonov ◽  
Paul Kessenich ◽  
Thomas C. Sideris
Keyword(s):  
Global Existence ◽  
Initial Value Problem ◽  
Strong Solutions ◽  
Small Displacement ◽  
Initial Value ◽  
Global Strong Solutions ◽  
Three Space

<p style='text-indent:20px;'>The initial value problem for incompressible Hookean viscoelastic motion in three space dimensions has global strong solutions with small displacements.</p>

scholarly journals The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhen Cheng ◽  
Wenjun Wang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Strong Solutions ◽  
Compressible Fluids ◽  
Existence Theory ◽  
Optimal Time ◽  
Two Phase ◽  
Frequency Decomposition ◽  
The Cauchy Problem ◽  
Global Strong Solutions

<p style='text-indent:20px;'>In this paper, we consider the global existence of the Cauchy problem for a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula>. We get the existence theory of global strong solutions by using the decaying properties of the solutions. The energy method combined with the low-high-frequency decomposition is used to derive such properties and hence the global existence. As a byproduct, the optimal time decay estimates of all-order spatial derivatives of the pressure and the velocity are obtained.</p>

scholarly journals Approximate solutions of equations defined by complex spherical multiplier operators

2005 ◽  
Vol 2005 (2) ◽  
pp. 93-115
Author(s):  
C. P. Oliveira
Keyword(s):  
Approximate Solutions ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Sobolev Type ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Solutions Of Equations ◽  
Multiplier Operators

This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.

Semi-local convergence of a Newton-like method for solving equations with a singular derivative

2018 ◽  
Vol 27 (1) ◽  
pp. 01-08
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
GEORGE SANTHOSH ◽  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Real Line ◽  
Local Convergence ◽  
Approximate Solutions ◽  
Convergence Domain ◽  
Solving Equations ◽  
Solutions Of Equations ◽  
Local Convergence Analysis ◽  
Special Case

We present a semi-local convergence analysis for a Newton-like method to approximate solutions of equations when the derivative is not necessarily non-singular in a Banach space setting. In the special case when the equation is defined on the real line the convergence domain is improved for this method when compared to earlier results. Numerical results where earlier results cannot apply but the new results can apply to solve nonlinear equations are also presented in this study.

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