scholarly journals On the Global Well-Posedness of the Viscous Two-Component Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Xiuming Li
Keyword(s):  
Global Existence ◽  
Existence Result ◽  
Well Posedness ◽  
Energy Identity ◽  
Two Component ◽  
Global Existence Result

We establish the local well-posedness for the viscous two-component Camassa-Holm system. Moreover, applying the energy identity, we obtain a global existence result for the system with(u0,η0)∈H1(ℝ)×L2(ℝ).

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

On a critical nonlinear problem involving the fractional Laplacian

2021 ◽  
pp. 2150066
Author(s):  
Azeb Alghanemi ◽  
Hichem Chtioui
Keyword(s):  
Global Existence ◽  
Bounded Domain ◽  
Nonlinear Problem ◽  
Fractional Laplacian ◽  
Existence Result ◽  
Counting Formula ◽  
Global Existence Result

Fractional Yamabe-type equations of the form [Formula: see text] in [Formula: see text] on [Formula: see text], where [Formula: see text] is a bounded domain of [Formula: see text], [Formula: see text] is a given function on [Formula: see text] and [Formula: see text], is the fractional Laplacian are considered. Bahri’s estimates in the fractional setting will be proved and used to establish a global existence result through an index-counting formula.

A Global Existence Result for Korteweg System in the Critical LP Framework

2019 ◽  
Vol 39 (6) ◽  
pp. 1639-1660
Author(s):  
Zhensheng Gao ◽  
Yan Liang ◽  
Zhong Tan
Keyword(s):  
Global Existence ◽  
Existence Result ◽  
Global Existence Result

Global Existence Result for the Generalized Peterlin Viscoelastic Model

2017 ◽  
Vol 49 (4) ◽  
pp. 2950-2964 ◽  
Author(s):  
Mária Lukáčová-Medviďová ◽  
Hana Mizerová ◽  
Šárka Nečasová ◽  
Michael Renardy
Keyword(s):  
Global Existence ◽  
Existence Result ◽  
Viscoelastic Model ◽  
Global Existence Result
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