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 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.

scholarly journals Remarks on the critical nonlinear high-order heat equation

2019 ◽  
Vol 26 (1/2) ◽  
pp. 127-152
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
High Order ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

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.

WELL-POSEDNESS AND BLOWUP PHENOMENA FOR A THREE-COMPONENT CAMASSA–HOLM SYSTEM WITH PEAKONS

2012 ◽  
Vol 09 (03) ◽  
pp. 451-467 ◽  
Author(s):  
QIAOYI HU ◽  
LIYUN LIN ◽  
JI JIN
Keyword(s):  
Initial Value Problem ◽  
Strong Solutions ◽  
Well Posedness ◽  
Initial Value ◽  
Blowup Rate ◽  
Holm Equation ◽  
Two Component

First, we establish the local well-posedness of the initial value problem for a new three-component Camassa–Holm system with peakons. We then present a precise blowup scenario and several blowup results for strong solutions to that system. Finally, we determine the blowup rate of strong solutions to the system when a blowup occurs. Our results include all earlier results on the Camassa–Holm equation and on a two-component Camassa–Holm system with peakons.

scholarly journals Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
M. B. Dhakne ◽  
Kishor D. Kucche
Keyword(s):  
Global Existence ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
A Priori ◽  
A Priori Bounds ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Fredholm Functional

AbstractIn the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

HOPF SOLUTIONS TO A FLUID-ELASTIC INTERACTION MODEL

2008 ◽  
Vol 18 (02) ◽  
pp. 215-269 ◽  
Author(s):  
M. GUIDORZI ◽  
M. PADULA ◽  
P. I. PLOTNIKOV
Keyword(s):  
Global Existence ◽  
Existence Theorem ◽  
Initial Value Problem ◽  
Interaction Model ◽  
Elastic Interaction ◽  
Initial Condition ◽  
Two Dimensional ◽  
Initial Value ◽  
Global Existence Theorem ◽  
Model Equations

In this paper, we give a global existence theorem of weak solutions to model equations governing interaction fluid structure in a two-dimensional layer, cf. Refs. 8 and 14. To our knowledge this is the first existence theorem of global in time solutions for such model. The interest of our result is double because, first, we change the original initial value problem by deleting one initial condition, second, we construct a solution through the classical Galerkin method for which several computing codes have been constructed.

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