Navier–Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

Navier–Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady... Consider the Navier–Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity $$-\,h(t)u_\infty $$ - h ( t ) u ∞ with constant vector $$u_\infty \in {\mathbb {R}}^3{\setminus }\{0\}$$ u ∞ ∈ R 3 \ { 0 } . Finn raised the question whether his steady solutions are attainable as limits for $$t\rightarrow \infty $$ t → ∞ of unsteady solutions starting from motionless state when $$h(t)=1$$ h ( t ) = 1 after some finite time and $$h(0)=0$$ h ( 0 ) = 0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307–318, 1997) for small $$u_\infty $$ u ∞ . We study some generalized situation in which unsteady solutions start from large motions being in $$L^3$$ L 3 . We then conclude that the steady solutions for small $$u_\infty $$ u ∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which $$h(t)=0$$ h ( t ) = 0 after some finite time and $$h(0)=1$$ h ( 0 ) = 1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large $$u_\infty $$ u ∞ is. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

Navier–Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

Loading next page...
 
/lp/springer_journal/navier-stokes-flow-past-a-rigid-body-attainability-of-steady-solutions-m71kt007VB
Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0344-3
Publisher site
See Article on Publisher Site

Abstract

Consider the Navier–Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity $$-\,h(t)u_\infty $$ - h ( t ) u ∞ with constant vector $$u_\infty \in {\mathbb {R}}^3{\setminus }\{0\}$$ u ∞ ∈ R 3 \ { 0 } . Finn raised the question whether his steady solutions are attainable as limits for $$t\rightarrow \infty $$ t → ∞ of unsteady solutions starting from motionless state when $$h(t)=1$$ h ( t ) = 1 after some finite time and $$h(0)=0$$ h ( 0 ) = 0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307–318, 1997) for small $$u_\infty $$ u ∞ . We study some generalized situation in which unsteady solutions start from large motions being in $$L^3$$ L 3 . We then conclude that the steady solutions for small $$u_\infty $$ u ∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which $$h(t)=0$$ h ( t ) = 0 after some finite time and $$h(0)=1$$ h ( 0 ) = 1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large $$u_\infty $$ u ∞ is.

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Nov 8, 2017

References

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
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

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off