On the existence of unique global-in-time solutions and temporal decay rates of solutions to some non-Newtonian incompressible fluids

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Hantaek Bae ◽  
Kyungkeun Kang
Keyword(s):  
Incompressible Fluids ◽  
Decay Rates ◽  
Temporal Decay

Temporal and spatial decays for the Navier–Stokes equations

2005 ◽  
Vol 135 (3) ◽  
pp. 461-478 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Temporal And Spatial

We obtain spatial and temporal decay rates of weak solutions of the Navier–Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by He and Xin in 2001 does not exceed 3/2;. However, we show the power can be extended up to 5/2;.

Decay rates for the solutions of model equations for bore propagation

1995 ◽  
Vol 125 (2) ◽  
pp. 371-398 ◽  
Author(s):  
S. V. Rajopadhye
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Burgers Equation ◽  
Decay Rates ◽  
Time Behaviour ◽  
Large Time Behaviour ◽  
Temporal Decay ◽  
De Vries ◽  
Model Equations

We study the large-time behaviour of solutions to the Korteweg-de Vries-Burgers equation with bore-like initial data. This work relies on the methods of Amick, Bona and Schonbeck to obtain sharp rates of temporal decay of certain norms of the solution, thus obtaining an improvement over results of Naumkin and Shishmarev.

Temporal and spatial decays for the Navier–Stokes equations

2005 ◽  
Vol 135 (3) ◽  
pp. 461-478 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Temporal And Spatial

We obtain spatial and temporal decay rates of weak solutions of the Navier–Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by He and Xin in 2001 does not exceed 3/2;. However, we show the power can be extended up to 5/2;.

Is grid turbulence Saffman turbulence?

2009 ◽  
Vol 642 ◽  
pp. 373-394 ◽  
Author(s):  
P.-Å. KROGSTAD ◽  
P. A. DAVIDSON
Keyword(s):  
Energy Decay ◽  
Decay Rates ◽  
Homogeneous Turbulence ◽  
Grid Turbulence ◽  
Temporal Decay ◽  
Dimensionless Energy ◽  
Integral Scales ◽  
Decay Exponent ◽  
Energy Decay Rates ◽  
Large Wind

There has been a longstanding debate as to whether the large scales in grid turbulence should be classified as of the Batchelor or Saffman type. In the former, the integral scales, u and ℓ, satisfy u2ℓ5 ≈ constant, while in Saffman turbulence we have u2ℓ3 = constant. For strictly homogeneous turbulence the energy decay rates in these two types of turbulence differ, with u2 ~ t−10/7 in Batchelor turbulence and u2 ~ t−6/5 in Saffman turbulence. We present high-resolution measurements of grid turbulence taken in a large wind tunnel. The particularly large test section allows us to measure energy decay exponents with high accuracy. We find that the turbulence behind the grid is almost certainly of the Saffman type, with u2ℓ3 = constant. The measured energy decay exponent, however, is found to lie slightly below the theoretical prediction of u2 ~ t−1.2. Rather we find u2 ~ t−n, with n = 1.13±0.02. This discrepancy is shown to arise from a weak temporal decay of the dimensionless energy dissipation coefficient, εℓ/u3, which is normally taken to be constant in strictly homogeneous turbulence, but which varies very slowly in grid turbulence.

scholarly journals Global Existence and Temporal Decay of Large Solutions for the Poisson--Nernst--Planck Equations in Low Regularity Spaces

2021 ◽  
Author(s):  
Jihong Zhao ◽  
Xilan Liu
Keyword(s):  
Global Existence ◽  
Decay Rates ◽  
Large Solution ◽  
Low Regularity ◽  
Charged Species ◽  
Temporal Decay ◽  
Large Solutions ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Positively Charged

We are concerned with the global existence and decay rates of large solutions for the Poisson–Nernst–Planck equations. Based on careful observation of algebraic structure of the equations and using the weighted Chemin–Lerner type norm, we obtain the global existence and optimal decay rates of large solutions without requiring the summation of initial densities of a negatively and positively charged species is small enough. Moreover, the large solution is obtained for initial data belonging to the low regularity Besov spaces with different regularity and integral indices for the different charged species, which indicates more specific coupling relations between the negatively and positively charged species.

Comparison of decay rates of faecal indicator organisms in recreational coastal water and sediment

2002 ◽  
Vol 2 (3) ◽  
pp. 131-138 ◽  
Author(s):  
D.L. Craig ◽  
H.J. Fallowfield ◽  
N.J. Cromar
Keyword(s):  
Water Column ◽  
Coastal Water ◽  
Decay Rates ◽  
Organic Carbon Content ◽  
Indicator Organisms ◽  
Filtration Method ◽  
E Coli ◽  
Water And Sediment ◽  
Increased Risk ◽  
High Organic Carbon Content

A laboratory based microcosm study utilising intact non-sterile sediment cores was undertaken to determine the survival of the faecal indicator organisms Escherichia coli, Enterococcus faecium and somatic coliphage in both recreational coastal water and sediment. Overlying water was inoculated with the test organisms and incubated at 10°C, 20°C or 30°C. E. coli, enterococcus and coliphage were enumerated from the water column and sediment by the membrane filtration method, Enterolert (IDEXX Laboratories) and the double-agar overlay methods respectively on days 0, 1, 2, 7, 14 and 28 following inoculation. It was demonstrated that for all organisms, greater decay (k; d-1) occurred in the water column compared to sediment. Sediment characteristics were found to influence decay, with lowest decay rates observed in sediment consisting of high organic carbon content and small particle size. Decay of E. coli was significantly greater in both the water column and sediment compared with enterococcus and coliphage under all conditions. Decay of enterococcus was found to closely resemble that of coliphage decay. Survival of all organisms was inversely related to temperature, with greatest decay at 30°C. However, increased temperature had a less significant impact on survival of enterococcus and coliphage compared with E. coli. The importance of this study for estimating risk from recreational exposure is great if some pathogenic microorganisms behave similarly to the organisms tested in this study. In particular if survival rates of pathogens are similar to enterococcus and coliphage, then their ability to accumulate in coastal sediment may lead to an increased risk of exposure if these organisms are resuspended into the water column due to natural turbulence or human recreational activity.

The Propagation of Shock Waves in Incompressible Fluids: The Case of Freshwater

2014 ◽  
Vol 132 (1) ◽  
pp. 427-437 ◽  
Author(s):  
Andrea Mentrelli ◽  
Tommaso Ruggeri
Keyword(s):  
Shock Waves ◽  
Incompressible Fluids
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