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Enhanced lifespan bounds for 1D quasilinear Klein-Gordon flows
Hongjing Huang, Mihaela Ifrim, Daniel Tataru
In this article we consider one-dimensional scalar quasilinear Klein--Gordon equations with general nonlinearities, on both and . By employing a refined mo…
Local well-posedness of the skew mean curvature flow for large data
Jiaxi Huang, Daniel Tataru
The skew mean curvature flow is an evolution equation for dimensional ma\-nifolds embedded in (or more generally, in a Riemannian manifold). It can be viewed…
Large data global well-posedness for the modified Novikov-Veselov system
Adrian Nachman, Peter Perry, Daniel Tataru
The modified Novikov-Veselov system (mNV) is a cubic third order dispersive evolution in two space dimensions. It is also completely integrable, belonging to the same hierarchy as…
Global solutions for cubic quasilinear ultrahyperbolic Schrödinger flows
Mihaela Ifrim, Ben Pineau, Daniel Tataru
In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global w…
Sharp well-posedness for the free boundary MHD equations
Mihaela Ifrim, Ben Pineau, Daniel Tataru +1
In this article, we provide a definitive well-posedness theory for the free boundary problem in incompressible magnetohyrodynamics. Despite the clear physical interest in this syst…
Local well-posedness of the Skew mean curvature flow for small data in dimensions
Jiaxi Huang, Daniel Tataru
The skew mean curvature flow is an evolution equation for dimensional manifolds embedded in (or more generally, in a Riemannian manifold). It can be viewed a…