# Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains

Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains Consider the steady neutron transport equation with diffusive boundary condition. In Wu and Guo (Commun Math Phys 336:1473–1553, 2015) and Wu et al. (J Stat Phys 165:585–644, 2016), it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish the diffusive limit for a 2D convex domain. Our contribution relies on novel weighted $${W^{1,\infty}}$$ W 1 , ∞ estimates for the Milne problem with geometric correction in the presence of a convex domain, as well as an $${L^{2m}-L^{\infty}}$$ L 2 m - L ∞ framework which yields stronger remainder estimates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

# Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains

, Volume 226 (1) – May 30, 2017
83 pages

/lp/springer_journal/geometric-correction-in-diffusive-limit-of-neutron-transport-equation-Hz8Pv37dqi
Publisher
Springer Berlin Heidelberg
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1135-y
Publisher site
See Article on Publisher Site

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve 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. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial