Carlos E. Kenig

most citedGlobal well-posedness of the Benjamin-Ono equation in low-regularity spaces

10 citations · 18 across the 6 of their papers we have counts for

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math.AP2005

Global wellposedness of the modified Benjamin-Ono equation with initial data in $H^{1/2}$

Carlos E. Kenig, Hideo Takaoka

We prove that the modified Benjamin-Ono equation is globally wellposed in $H^{s}$ for $s \geq 1/2$ .

math.AP2005

Decay at infinity of caloric functions within characteristic hyperplanes

L. Escauriaza, C. E. Kenig, G. Ponce +1

It is shown that a function $u$ satisfying, $∣Δ u + \partial_{t} u ∣ \leq M (∣ u ∣ + ∣\nabla u ∣)$ , $∣ u (x, t) ∣ \leq M e^{M ∣ x ∣^{2}}$ in $R^{n} \times [0, T]$ and $∣ u (x, 0) ∣ \leq C_{k} e^{- k ∣ x ∣^{2}}$ in $R^{n}$ and…

math.AP2005★ 10 cited

Global well-posedness of the Benjamin-Ono equation in low-regularity spaces

Alexandru Ionescu, Carlos Kenig

We prove that the Benjamin-Ono initial value problem is globally well-posed in the Sobolev spaces $H_{r}^{σ}$ , $σ \geq 0$ .

math.AP2005★ 6 cited

The General Quasilinear Ultrahyperbolic Schrödinger Equation

C. E. Kenig, G. Ponce, C. Rolvung +1

In this work we establish a local existence theory for the initial value problem associated to the general quasi-linear ultrahyperbolic Schrödinger equation.

math.AP2005★ 2 cited

Variable coefficient Schrödinger flows for ultrahyperbolic operators

C. E. Kenig, G. Ponce, C. Rolvung +1

In this paper we study the local solvability of nonlinear Schrödinger equations of the form $$\p_t u = i {\cal L}(x) u + \vec b_1(x)\cdot \nabla_x u + \vec b_2(x)\cdot \nabla_x \ba…

math.AP2004

The Calderón problem with partial data

C. E. Kenig, J. Sjoestrand, G. Uhlmann

In this paper we improve an earlier result by Bukhgeim and Uhlmann, by showing that in dimension larger than or equal to three, the knowledge of the Cauchy data for the Schrödinger…