Daniel Tataru

STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS

ABSTRACT We prove Strichartz type estimates for the Schrödinger equation corresponding to a second order elliptic operator with variable coefficients. We assume that the coefficients are a C 2 compactly supported perturbation of the identity, satisfying a nontrapping condition.

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from ℝ2+1→S2 of the form

Local and global results for wave maps I

u(t,r)=Q(\lambda(t)r)+\mathcal{R}(t,r)

Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III

where u is the polar angle on the sphere,

Local decay of waves on asymptotically flat stationary space-times

Q(r)=2\arctan r

Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation

is the ground state harmonic map, λ(t)=t-1-ν, and

Regularity of Wave-Maps in Dimension 2 + 1

\mathcal{R}(t,r)

Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation

is a radiative error with local energy going to zero as t→0. The number

Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions

\nu>\frac{1}{2}

Global well-posedness of the KP-I initial-value problem in the energy space

can be prescribed arbitrarily. This is accomplished by first “renormalizing” the blow-up profile, followed by a perturbative analysis.