19 citations · 29 across the 6 of their papers we have counts for
4 papers · 1 filter
Blow up dynamics for the 3D energy-critical Nonlinear Schrödinger equation
Tobias Schmid
We construct a two-parameter continuum of type II blow up solutions for the energy-critical focusing NLS in dimension . The solutions collapse to a single energy bubble in…
Global results for a Cauchy problem related to biharmonic wave maps
Tobias Schmid
We prove global existence of a derivative bi-harmonic wave equation with a non-generic quadratic nonlinearity and small initial data in the scaling critical space $\dot{B}^{2,1}_{\…
Energy bounds for a fourth-order equation in low dimensions related to wave maps
Tobias Schmid
For compact, isometrically embedded Riemannian manifolds , we introduce a fourth-order version of the wave map equation. By energy estimates, we pr…
Biharmonic wave maps: Local wellposedness in high regularity
Sebastian Herr, Tobias Lamm, Tobias Schmid +1
We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the sol…