Petr Plechác and Vladimír Sverák 2003 Nonlinearity 16 2083 doi:10.1088/0951-7715/16/6/313
Petr Plechác1 and Vladimír Sverák2
Show affiliationsRecommended by E S Titi
We study a dissipative nonlinear equation modelling certain features of the Navier–Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions n≤4. For dimensions n>4, we present strong numerical evidence supporting the existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding the existence of self-similar singular solutions to a semi-linear heat equation.
02.30.Jr Partial differential equations
47.10.ad Navier-Stokes equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
34B16 Singular nonlinear boundary value problems
Issue 6 (November 2003)
Received 12 February 2003, in final form 1 July 2003
Published 5 September 2003
Petr Plechác and Vladimír Sverák 2003 Nonlinearity 16 2083
Pål Erik Goa et al 2001 Supercond. Sci. Technol. 14 729
Brian R Hunt and Vadim Yu Kaloshin 1997 Nonlinearity 10 1031
Xin He Meng and Peng Wang 2004 Class. Quantum Grav. 21 951
Natalia Denisova 2004 Plasma Sources Sci. Technol. 13 531
Ildar Gabitov and Ian Marshall 1998 Nonlinearity 11 845
David T Burns et al 2007 Metrologia 44 L53
G Penn et al 2003 J. Phys. G: Nucl. Part. Phys. 29 1719
Salvatore Ganci 2009 Phys. Educ. 44 569
R B Frenkel 2009 Metrologia 46 661