In the present paper we study the convergence of the solution of the two dimensional (2-D) stochastic Leray- $$\alpha $$ α model to the solution of the 2-D stochastic Navier–Stokes equations. We are mainly interested in the rate, as $$\alpha \rightarrow 0$$ α → 0 , of the following error function $$\begin{aligned} \varepsilon _\alpha (t)=\sup _{s\in [0,t]} |\mathbf {u}^\alpha (s)-\mathbf {u}(s)|+\left( \int _0^t |\mathrm {A}^\frac{1}{2}[\mathbf {u}^\alpha (s)-\mathbf {u}(s)] |^2 ds \right) ^\frac{1}{2}, \end{aligned}$$ ε α ( t ) = sup s ∈ [ 0 , t ] | u α ( s ) - u ( s ) | + ∫ 0 t | A 1 2 [ u α ( s ) - u ( s ) ] | 2 d s 1 2 , where $$\mathbf {u}^\alpha $$ u α and $$\mathbf {u}$$ u are the solution of stochastic Leray- $$\alpha $$ α model and the stochastic Navier–Stokes equations, respectively. We show that when properly localized the error function $$\varepsilon _\alpha $$ ε α converges in mean square as $$\alpha \rightarrow 0$$ α → 0 and the convergence is of order $$O(\alpha )$$ O ( α ) . We also prove that $$\varepsilon _\alpha $$ ε α converges in probability to zero with order at most $$O(\alpha )$$ O ( α ) .
Applied Mathematics and Optimization – Springer Journals
Published: Jun 16, 2015
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”
Daniel C.
“Whoa! It’s like Spotify but for academic articles.”
@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”
@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”
@JoseServera
DeepDyve Freelancer | DeepDyve Pro | |
---|---|---|
Price | FREE | $49/month |
Save searches from | ||
Create lists to | ||
Export lists, citations | ||
Read DeepDyve articles | Abstract access only | Unlimited access to over |
20 pages / month | ||
PDF Discount | 20% off | |
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.
ok to continue