arXiv subjects

Dirk Blomker

Publications and source records attributed to Dirk Blomker.

3 recordsLinked to original sources

arXiv2010

Local existence and uniqueness in the largest critical space for a surface growth model

We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to scaling and we prove our results in the largest possible critical space such that weak solutions are defined. The uniqueness of global weak solutions remains unfortunately open, unless the initial conditions are sufficiently small.

math.AP↗

arXiv2009

Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity

The qualitative properties of local random invariant manifolds for stochastic partial differential equations with quadratic nonlinearities and multiplicative noise is studied by a cut off technique. By a detail estimates on the Perron fixed point equation describing the local random invariant manifold, the structure near a bifurcation is given.

math.DS↗

arXiv2009

Regularity and blow-up in a surface growth model

The paper contains several regularity results and blow-up criterions 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.

math.AP↗