scholarly journals Lr-LpStability of the Incompressible Flows with Nonzero Far-Field Velocity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Jaiok Roh
Keyword(s):  
Constant Velocity ◽  
Incompressible Flows ◽  
Temporal Stability ◽  
Stationary Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Far Field ◽  
Spatial Direction ◽  
Field Velocity ◽  
The Stability

We consider the stability of stationary solutionswfor the exterior Navier-Stokes flows with a nonzero constant velocityu∞at infinity. Foru∞=0with nonzero stationary solutionw, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability inLpspaces for1<pand obtained good stability decay rates. For the spatial direction, we recently obtained some results. Foru∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability inL2space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability inLpspaces forp≥3. Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense. In this paper, we improve Bae and Roh's result in the spacesLpforp>1and obtainLr-Lpstability as Kozono and Ogawa and Borchers and Miyakawa obtained foru∞=0.

The exponential behavior and stabilizability of the stochastic 3D Navier–Stokes equations with damping

2019 ◽  
Vol 31 (07) ◽  
pp. 1950023 ◽  
Author(s):  
Hui Liu ◽  
Lin Lin ◽  
Chengfeng Sun ◽  
Qingkun Xiao
Keyword(s):  
Weak Solutions ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Exponential Behavior ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
The Mean ◽  
The Stability

The stochastic 3D Navier–Stokes equation with damping driven by a multiplicative noise is considered in this paper. The stability of weak solutions to the stochastic 3D Navier–Stokes equations with damping is proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions are proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The stabilization of these equations is obtained for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text].

scholarly journals CONVERGENCE RATE FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH EXTERNAL FORCE

2006 ◽  
Vol 03 (03) ◽  
pp. 561-574 ◽  
Author(s):  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Convergence Rate ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Optimal Convergence Rate ◽  
Potential Force ◽  
Stationary Potential ◽  
Navier Stokes Equations ◽  
The Stability ◽  
External Forces

For the compressible Navier–Stokes equations with a stationary potential force, the stability of the stationary solutions was studied by Matsumura and Nishida. The convergence rate to the stationary solutions in time was later studied by Deckelnick which was improved by Shibata and Tanaka for more general external forces. This paper deals with the case for the stationary potential force under some smallness condition, to establish an almost optimal convergence rate in L2(ℝN)-norm for N ≥ 3.

scholarly journals Asymptotic Behavior of the Navier-Stokes Equations with Nonzero Far-Field Velocity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Jaiok Roh
Keyword(s):  
Stokes Equations ◽  
Temporal Stability ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Weighted Function ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Field Velocity ◽  
Temporal Rate

Concerning the nonstationary Navier-Stokes flow with a nonzero constant velocity at infinity, the temporal stability has been studied by Heywood (1970, 1972) and Masuda (1975) inL2space and by Shibata (1999) and Enomoto-Shibata (2005) inLpspaces forp≥3. However, their results did not include enough information to find the spatial decay. So, Bae-Roh (2010) improved Enomoto-Shibata's results in some sense and estimated the spatial decay even though their results are limited. In this paper, we will prove temporal decay with a weighted function by usingLr-Lpdecay estimates obtained by Roh (2011). Bae-Roh (2010) proved the temporal rate becomes slower by(1+σ)/2if a weighted function is|x|σfor0<σ<1/2. In this paper, we prove that the temporal decay becomes slower byσ,where0<σ<3/2if a weighted function is|x|σ. For the proof, we deduce an integral representation of the solution and then establish the temporal decay estimates of weightedLp-norm of solutions. This method was first initiated by He and Xin (2000) and developed by Bae and Jin (2006, 2007, 2008).

Implications of Person Fluctuation for the Stability and Validity of Test Scores

Methodology ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 142-148 ◽  
Author(s):  
Pere J. Ferrando
Keyword(s):  
Item Response ◽  
Test Scores ◽  
Temporal Stability ◽  
Person Fit ◽  
Item Parameters ◽  
Individual Trait ◽  
The Stability ◽  
The Individual ◽  
Different Levels ◽  
Fluctuation Model

In the IRT person-fluctuation model, the individual trait levels fluctuate within a single test administration whereas the items have fixed locations. This article studies the relations between the person and item parameters of this model and two central properties of item and test scores: temporal stability and external validity. For temporal stability, formulas are derived for predicting and interpreting item response changes in a test-retest situation on the basis of the individual fluctuations. As for validity, formulas are derived for obtaining disattenuated estimates and for predicting changes in validity in groups with different levels of fluctuation. These latter formulas are related to previous research in the person-fit domain. The results obtained and the relations discussed are illustrated with an empirical example.

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Influence of Tsunami Aspect Ratio on Near and Far-Field Tsunami Amplitude

Geosciences ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 178
Author(s):  
Natalia K. Sannikova ◽  
Harvey Segur ◽  
Diego Arcas
Keyword(s):  
Aspect Ratio ◽  
Near Field ◽  
Decay Rates ◽  
Far Field ◽  
Present Evidence ◽  
Positive Wave ◽  
Initial Wave ◽  
N Wave ◽  
Tsunami Amplitude ◽  
Wave Shapes

This study presents a numerical investigation of the source aspect ratio (AR) influence on tsunami decay characteristics with an emphasis in near and far-field differences for two initial wave shapes Pure Positive Wave and N-wave. It is shown that, when initial total energy for both tsunami types is kept the same, short-rupture tsunami with more concentrated energy are likely to be more destructive in the near-field, whereas long rupture tsunami are more dangerous in the far-field. The more elongated the source is, the stronger the directivity and the slower the amplitude decays in the intermediate- and far-fields. We present evidence of this behavior by comparing amplitude decay rates from idealized sources and showing their correlation with that observed in recent historical events of similar AR.

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