Finite-time blow-up of solutions of an aggregation equation in Rn

被引：94

作者：

Bertozzi, Andrea L. ^{[1
]}

Laurent, Thomas

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2007年 / 274卷 / 03期

关键词：

D O I：

10.1007/s00220-007-0288-1

中图分类号：

O4 [物理学];

学科分类号：

0702 [物理学];

摘要：

We consider the aggregation equation u(t) + del (.) (u del K * u) = 0 in R-n, n >= 2, where K is a rotationally symmetric, nonnegative decaying kernel with a Lipschitz point at the origin, e.g. K(x) = e(-vertical bar x vertical bar). We prove finite-time blow-up of solutions from specific smooth initial data, for which the problem is known to have short time existence of smooth solutions.

引用

页码：717 / 735

页数：19

共 29 条

[1]

REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS [J].

BEALE, JT ;

KATO, T ;

MAJDA, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 94 (01) :61-66

[2]

An integro-differential equation arising as a limit of individual cell-based models [J].

Bodnar, M ;

Velazquez, JJL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 222 (02) :341-380

[3]

Diffusion, attraction and collapse [J].

Brenner, MP ;

Constantin, P ;

Kadanoff, LP ;

Schenkel, A ;

Venkataramani, SC .

NONLINEARITY, 1999, 12 (04) :1071-1098

[4]

Burger M, 2007, REAL WORLD APPL, V8

[5]

BURGER M, 2006, LARGE TIME BEHAV NON

[6]

Chandrasekhar S., 1967, An introduction to the study of stellar structure

[7]

Chuang Yao-li., 2006, State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System

[8]

A SIMPLE ONE-DIMENSIONAL MODEL FOR THE 3-DIMENSIONAL VORTICITY EQUATION [J].

CONSTANTIN, P ;

LAX, PD ;

MAJDA, A .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (06) :715-724

[9]

GEOMETRIC STATISTICS IN TURBULENCE [J].

CONSTANTIN, P .

SIAM REVIEW, 1994, 36 (01) :73-98

[10]

FORMATION OF STRONG FRONTS IN THE 2-D QUASI-GEOSTROPHIC THERMAL ACTIVE SCALAR [J].

CONSTANTIN, P ;

MAJDA, AJ ;

TABAK, E .

NONLINEARITY, 1994, 7 (06) :1495-1533

← 1 2 3 →