Dynamics of Partial Differential Equations

Volume 6 (2009)

Number 3

Regularity and blow up in a surface growth model

Pages: 227 – 252

DOI: https://dx.doi.org/10.4310/DPDE.2009.v6.n3.a2


Dirk Blömker (Institut für Mathematik, Universität Augsburg, Germany)

Marco Romito (Dipartimento di Matematica, Università di Firenze, Italy)


he paper contains several regularity results and blow-up criteria for a surface growth model, which seems to have similar properties to the 3D Navier-Stokes, although it is a scalar equation. As a starting point we focus on energy methods and Lyapunov-functionals.


surface growth, critical space, uniqueness, regularity, blow up, Leray estimates, Lyapunov function

2010 Mathematics Subject Classification

35B33, 35B45, 35B65, 35K55, 35Qxx, 60H15

Published 1 January 2009