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Volume 19, Issue 4
A Note on L^2 Decay of Ladyzhenskaya Model

Boqing Dong

J. Part. Diff. Eq., 19 (2006), pp. 304-318.

Published online: 2006-11

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  • Abstract

This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth (p ≥ 3) in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L²(R^3) norm like t!n^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2}) under the initial data u_0 ∈ L²(R^3) ∩ L^r(R^3) for 1 ≤ r ‹ 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.

  • Keywords

Ladyzhenskaya model L² decay spectral decomposition

  • AMS Subject Headings

35B40 35Q35 76A05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-19-304, author = {}, title = {A Note on L^2 Decay of Ladyzhenskaya Model}, journal = {Journal of Partial Differential Equations}, year = {2006}, volume = {19}, number = {4}, pages = {304--318}, abstract = {

This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth (p ≥ 3) in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L²(R^3) norm like t!n^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2}) under the initial data u_0 ∈ L²(R^3) ∩ L^r(R^3) for 1 ≤ r ‹ 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5334.html} }
TY - JOUR T1 - A Note on L^2 Decay of Ladyzhenskaya Model JO - Journal of Partial Differential Equations VL - 4 SP - 304 EP - 318 PY - 2006 DA - 2006/11 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5334.html KW - Ladyzhenskaya model KW - L² decay KW - spectral decomposition AB -

This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth (p ≥ 3) in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L²(R^3) norm like t!n^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2}) under the initial data u_0 ∈ L²(R^3) ∩ L^r(R^3) for 1 ≤ r ‹ 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.

Boqing Dong . (2019). A Note on L^2 Decay of Ladyzhenskaya Model. Journal of Partial Differential Equations. 19 (4). 304-318. doi:
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