Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Editorial

Editorial Ann Univ Ferrara (2009) 55:195–197 DOI 10.1007/s11565-009-0081-5 Reinhard Farwig · Jiri ˇ Neustupa · Patrick Penel Published online: 17 October 2009 © Università degli Studi di Ferrara 2009 The mathematical theory of the Navier–Stokes equations poses—since the pioneering work of Jean Leray in 1934—a famous open problem for instationary solutions in three dimensions: It is unknown whether the so-called weak solution which does exist globally in time is regular or smooth for all times if the initial data is regular and large. Analogously, it is open whether a regular solution which can be constructed on a sufficiently small time interval does exist globally in time. Due to its utmost importance for the theory of nonlinear partial differential equations and applications in fluid mechanics this open problem is one of the seven Millennium Prize Problems of Clay Mathematics Institute, formulated in 2000. It is well-known that, given a domain  ⊂ R , a time interval (0, T ), an external 2 2 force field f ∈ L on  × (0, T ) and an initial value u ∈ L , there exists at least one weak solution in the energy class (the Leray–Hopf class) ∞ 2 2 1 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

Editorial

Download PDF
3 pages

Loading next page...
 
/lp/springer-journals/editorial-ALXWe93eqH
Publisher
Springer Journals
Copyright
Copyright © 2009 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-009-0081-5
Publisher site
See Article on Publisher Site

Abstract

Ann Univ Ferrara (2009) 55:195–197 DOI 10.1007/s11565-009-0081-5 Reinhard Farwig · Jiri ˇ Neustupa · Patrick Penel Published online: 17 October 2009 © Università degli Studi di Ferrara 2009 The mathematical theory of the Navier–Stokes equations poses—since the pioneering work of Jean Leray in 1934—a famous open problem for instationary solutions in three dimensions: It is unknown whether the so-called weak solution which does exist globally in time is regular or smooth for all times if the initial data is regular and large. Analogously, it is open whether a regular solution which can be constructed on a sufficiently small time interval does exist globally in time. Due to its utmost importance for the theory of nonlinear partial differential equations and applications in fluid mechanics this open problem is one of the seven Millennium Prize Problems of Clay Mathematics Institute, formulated in 2000. It is well-known that, given a domain  ⊂ R , a time interval (0, T ), an external 2 2 force field f ∈ L on  × (0, T ) and an initial value u ∈ L , there exists at least one weak solution in the energy class (the Leray–Hopf class) ∞ 2 2 1

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Oct 17, 2009

There are no references for this article.