126 citations · 387 across the 34 of their papers we have counts for
39 papers
The sharp lifespan for a system of multiple speed wave equations: Radial case
Marvin Koonce, Jason Metcalfe
Ohta examined a system of multiple speed wave equations with small initial data and demonstrated a finite time blowup. We show, in the radial case, that the same system exists almo…
Global existence for quasilinear wave equations satisfying the null condition
Michael Facci, Jason Metcalfe
We explore the global existence of solutions to systems of quasilinear wave equations satisfying the null condition when the initial data are sufficiently small. We adapt an approa…
On a System of Weakly Null Semilinear Equations
Jason Metcalfe, Alexander Stewart
We develop a new method for addressing certain weakly null systems of wave equations. This approach does not rely on Lorentz invariance nor on the use of null foliations, both of w…
Long-time existence for systems of quasilinear wave equations
Jason Metcalfe, Taylor Rhoads
We consider quasilinear wave equations in -dimensions where the nonlinearity is permitted to depend on the solution rather than just its derivatives. For scalar…
On the interaction of metric trapping and a boundary
Kiril Datchev, Jason Metcalfe, Jacob Shapiro +1
By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as…
Quasilinear Schrödinger equations III: Large Data and Short Time
Jeremy L. Marzuola, Jason Metcalfe, Daniel Tataru
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large data general quasilinear Schrödinger equations with a non-trapping assumption. T…