A global existence result for a spatially extended 3D Navier-Stokes problem with non-small initial data

2000 ◽  
Vol 7 (4) ◽  
pp. 415-434 ◽  
Author(s):  
Daniela Peterhof ◽  
Guido Schneider
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence Result ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Small Initial Data ◽  
Spatially Extended ◽  
Global Existence Result

scholarly journals GLOBAL CHARACTERISTIC PROBLEM FOR EINSTEIN VACUUM EQUATIONS WITH SMALL INITIAL DATA: (I) THE INITIAL DATA CONSTRAINTS

2005 ◽  
Vol 02 (01) ◽  
pp. 201-277 ◽  
Author(s):  
GIULIO CACIOTTA ◽  
FRANCESCO NICOLÒ
Keyword(s):  
Initial Data ◽  
Existence Result ◽  
Subsequent Paper ◽  
Small Initial Data ◽  
Asymptotic Decay ◽  
Characteristic Problem ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
Data Constraints ◽  
Global Existence Result

We show how to prescribe the initial data of a characteristic problem satisfying the constraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in detail the construction of the initial data and give a sketch of the existence result. This proof, which mimicks the analogous one for the non-characteristic problem in [19], will be the content of a subsequent paper.

scholarly journals L2-CONCENTRATION PHENOMENON FOR ZAKHAROV SYSTEM BELOW ENERGY NORM

2009 ◽  
Vol 11 (01) ◽  
pp. 27-57 ◽  
Author(s):  
DAOYUAN FANG ◽  
SIJIA ZHONG
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence Result ◽  
Space Dimension ◽  
Blow Up ◽  
Energy Norm ◽  
Zakharov System ◽  
Concentration Result ◽  
Global Existence Result ◽  
Concentration Phenomenon

In this paper, we prove an L2-concentration result of Zakharov system in space dimension two, with radial initial data [Formula: see text], when blow up of the solution happens by I-method. In addition to that, we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain's to the above-mentioned spaces.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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
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