T. Cazenave

activity

20102020

most citedContinuous dependence for NLS in fractional order spaces

55 citations · 323 across the 21 of their papers we have counts for

collaborators

21 papers

math.AP2020★ 24 cited

Asymptotic behavior for a dissipative nonlinear Schrödinger equation

Thierry Cazenave, Zheng Han, Ivan Naumkin

We consider the Schrödinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +Δu=λ|u|^αu \end{equation*} in $R^{N}$ , $N \geq 1$ , where $λ\in {\mathbb C}…

math.AP2020★ 5 cited

Sign-changing solutions of the nonlinear heat equation with persistent singularities

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We study the existence of sign-changing solutions to the nonlinear heat equation $\partial_{t} u = Δ u + ∣ u ∣^{α} u$ on $R^{N}$ , $N \geq 3$ , with $\frac{2}{N - 2} < α < α_{0}$ , where…

math.AP2019★ 4 cited

Local smooth solutions of the nonlinear Klein-gordon equation

Thierry Cazenave, Ivan Naumkin

Given any $μ_{1}, μ_{2} \in C$ and $α > 0$ , we prove the local existence of arbitrarily smooth solutions of the nonlinear Klein-Gordon equation $\partial_{ tt } u - Δu + μ_1 u =…

math.AP2019★ 15 cited

Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation

Thierry Cazenave, Zheng Han

We study the time-asymptotic behavior of solutions of the Schrödinger equation with nonlinear dissipation \begin{equation*} \partial _t u = i Δu + λ|u|^αu \end{equation*} in ${\mat…

math.AP2019★ 6 cited

Blowup on an arbitrary compact set for a Schödinger equation with nonlinear source term

Thierry Cazenave, Zheng Han, Yvan Martel

We consider the nonlinear Schrödinger equation on $R^{N}$ , $N \geq 1$ , \begin{equation*} \partial _t u = i Δu + λ| u |^αu \quad \mbox{on $R^{N}$ , $α > 0$ ,} \end{equat…

math.AP2019★ 2 cited

Solutions with prescribed local blow-up surface for the nonlinear wave equation

Thierry Cazenave, Yvan Martel, Lifeng Zhao

We prove that any sufficiently differentiable space-like hypersurface of $R^{1 + N}$ coincides locally around any of its points with the blow-up surface of a finite-energy…

math.AP2018★ 5 cited

Solutions blowing up on any given compact set for the energy subcritical wave equation

Thierry Cazenave, Yvan Martel, Lifeng Zhao

We consider the focusing energy subcritical nonlinear wave equation $\partial_{tt} u - Δ u = ∣ u ∣^{p - 1} u$ in $R^{N}$ , $N \geq 1$ . Given any compact set $ E \subset {\mathbb R}^…

math.AP2018★ 14 cited

Finite-time blowup for a Schrödinger equation with nonlinear source term

Thierry Cazenave, Yvan Martel, Lifeng Zhao

We consider the nonlinear Schrödinger equation \[ u_t = i Δu + | u |^αu \quad \mbox{on $R^{N}$ , $α > 0$ ,} \] for $H^{1}$ -subcritical or critical nonlinearities: $(N - 2) α \leq 4$ …

math.AP2018★ 6 cited

Perturbations of self-similar solutions

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_{t} = Δ u + ∣ u ∣^{α} u$ with $α > 0$ , either on $R^{N}$ , $N \geq 1$ , or on a bounded domain with Dirichlet boundary conditions. We prove th…

math.AP2017★ 11 cited

Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_{t} - Δ u = ∣ u ∣^{α} u$ on $R^{N}$ , where $α > 0$ and $N \geq 1$ . We prove that in the range $0 < α < \frac{4}{N - 2}$ , for every $μ > 0$ , there…

math.AP2017★ 50 cited

Modified scattering for the critical nonlinear Schrödinger equation

Thierry Cazenave, Ivan Naumkin

We consider the nonlinear Schrödinger equation $i u_{t} + Δ u = λ ∣ u ∣^{\frac{2}{N}} u$ in all dimensions $N \geq 1$ , where $λ \in C$ and $ℑ λ \leq 0$ . We construct a class of i…

math.AP2016★ 36 cited

Local existence, global existence, and scattering for the nonlinear Schrödinger equation

Thierry Cazenave, Ivan Naumkin

In this paper, we construct for every $α > 0$ and $λ \in C$ a space of initial values for which there exists a local solution of the nonlinear Schrödinger equation \begin{eq…

math.AP2016★ 3 cited

Finite-time blowup for some nonlinear complex Ginzburg-Landau equations

Thierry Cazenave, Seifeddine Snoussi

In this article, we review finite-time blowup criteria for the family of complex Ginzburg-Landau equations $u_{t} = e^{i θ} [Δ u + ∣ u ∣^{α} u] + γ u$ on $R^{N}$ , where $0 \le θ\le…

math.AP2015★ 10 cited

A Fujita-type blowup result and low energy scattering for a nonlinear Schrö\-din\-ger equation

Thierry Cazenave, Simão Correia, Flávio Dickstein +1

In this paper we consider the nonlinear Schrö\-din\-ger equation $i u_{t} + Δ u + κ ∣ u ∣^{α} u = 0$ . We prove that if $α < \frac{2}{N}$ and $ℑ κ < 0$ , then every nontrivial $H^{1}$ -solution blow…

math.AP2015★ 4 cited

Non-regularity in Hölder and Sobolev spaces of solutions to the semilinear heat and Schrödinger equations

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

In this paper we study the Cauchy problem for the semilinear heat and Schrödinger equations, with the nonlinear term $f (u) = λ ∣ u ∣^{α} u$ . We show that low regularity of $f$ (i.e.,…

math.AP2013★ 18 cited

Finite-time blowup for a complex Ginzburg-Landau equation with linear driving

Thierry Cazenave, João Paulo Dias, Mário Figueira

In this paper, we consider the complex Ginzburg--Landau equation $u_{t} = e^{i θ} [Δ u + ∣ u ∣^{α} u] + γ u$ on $R^{N}$ , where $α > 0$ , $γ \in R$ and $- π /2 < θ < π /2$ . By convexity argume…

math.AP2013

Local well-posedness for the $H^{2}$ -critical nonlinear Schrödinger equation

Thierry Cazenave, Daoyuan Fang, Zheng Han

In this paper, we consider the nonlinear Schrödinger equation $i u_{t} + Δ u = λ ∣ u ∣^{\frac{4}{N - 4}} u$ in $R^{N}$ , $N \geq 5$ , with $λ\in \C$. We prove local well-posedness (local existe…

math.AP2013★ 13 cited

Standing waves of the complex Ginzburg-Landau equation

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation $ϕ_{t} = e^{i θ} Δ ϕ + e^{iγ} ∣ ϕ ∣^{α} ϕ$ with periodic boundary conditions. Our result…

math.AP2012★ 36 cited

Finite-time blowup for a complex Ginzburg-Landau equation

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{- i θ} u_{t} = Δ u + ∣ u ∣^{α} u$ blow up in finite time, where α>0 and π/2<θ<π/2. For a fixed initial val…

math.AP2011★ 6 cited

Scattering for the focusing energy-subcritical NLS

Daoyuan Fang, Jian Xie, Thierry Cazenave

For the 3D focusing cubic nonlinear Schrodinger equation, Scattering of $H^{1}$ solutions inside the (scale invariant) potential well was established by Holmer and Roudenko~\cite{HR2…

math.AP2010★ 55 cited

Continuous dependence for NLS in fractional order spaces

Thierry Cazenave, Daoyuan Fang, Zheng Han

We consider the Cauchy problem for the nonlinear Schrödinger equation $i u_{t} + Δ u + λ ∣ u ∣^{α} u = 0$ in $R^{N}$ , in the $H^{s}$ -subcritical and critical cases $0 < α \leq 4/ (N - 2 s)$ , where $0<s<N/…

Asymptotic behavior for a dissipative nonlinear Schrödinger equation

Sign-changing solutions of the nonlinear heat equation with persistent singularities

Local smooth solutions of the nonlinear Klein-gordon equation

Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation

Blowup on an arbitrary compact set for a Schödinger equation with nonlinear source term

Solutions with prescribed local blow-up surface for the nonlinear wave equation

Solutions blowing up on any given compact set for the energy subcritical wave equation

Finite-time blowup for a Schrödinger equation with nonlinear source term

Perturbations of self-similar solutions

Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value

Modified scattering for the critical nonlinear Schrödinger equation

Local existence, global existence, and scattering for the nonlinear Schrödinger equation

Finite-time blowup for some nonlinear complex Ginzburg-Landau equations

A Fujita-type blowup result and low energy scattering for a nonlinear Schrö\-din\-ger equation

Non-regularity in Hölder and Sobolev spaces of solutions to the semilinear heat and Schrödinger equations

Finite-time blowup for a complex Ginzburg-Landau equation with linear driving

Local well-posedness for the H2-critical nonlinear Schrödinger equation

Standing waves of the complex Ginzburg-Landau equation

Finite-time blowup for a complex Ginzburg-Landau equation

Scattering for the focusing energy-subcritical NLS

Continuous dependence for NLS in fractional order spaces

Local well-posedness for the $H^{2}$ -critical nonlinear Schrödinger equation