# Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation

@article{Coz2014MinimalMB, title={Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation}, author={Stefan Le Coz and Yvan Martel and Pierre Raphael}, journal={arXiv: Analysis of PDEs}, year={2014} }

We consider a nonlinear Schr\"odinger equation with double power nonlinearity, where one power is focusing and mass critical and the other mass sub-critical. Classical variational arguments ensure that initial data with mass less than the mass of the ground state of the mass critical problem lead to global in time solutions. We are interested by the threshold dynamic and in particular by the existence of finite time blow up minimal solutions. For the mass critical problem, such an object exists…

## 30 Citations

Minimal mass blow-up solutions for nonlinear Schr\"{o}dinger equations with an inverse potential

- Mathematics
- 2020

in R . From the classical argument, the solution with subcritical mass (‖u‖2 < ‖Q‖2) is global and bounded in H(R ). Here, Q is the ground state of the mass-critical problem. Therefore, we are…

Minimal mass blow-up solutions for double power nonlinear Schr\"{o}dinger equations with an inverse potential

- Mathematics
- 2021

We consider the following nonlinear Schrödinger equation with double power nonlinearlities and an inverse power potential: i ∂u ∂t +∆u+ |u| 4 N u± C1|u| u± C2 |x|2σ u = 0 in R . From the classical…

Minimal mass blow-up solutions for nonlinear Schr\"{o}dinger equations with a singular potential

- Mathematics
- 2021

We consider the following nonlinear Schrödinger equation with an inverse potential: i ∂u ∂t +∆u+ |u| 4 N u± 1 |x|2σ log |x|u = 0 in R . From the classical argument, the solution with subcritical mass…

Mass concentration for nonlinear Schrödinger equation with partial confinement

- Mathematics
- 2020

Abstract This paper studies the dynamical properties of blow-up solutions for nonlinear Schrodinger equation with partial confinement, which may model the Bose-Einstein condensate under a partial…

Remarks on minimal mass blow up solutions for a double power nonlinear Schr\"{o}dinger equation

- Physics, Mathematics
- 2020

We consider the following nonlinear Schrodinger equation with double power nonlinearity \[ i\frac{\partial u}{\partial t}+\Delta u+|u|^{\frac{4}{N}}u+|u|^{p-1}u=0,\quad 1<p<1+\frac{4}{N} \] in…

STRONGLY INTERACTING BLOW UP BUBBLES FOR THE MASS CRITICAL NLS

- Mathematics
- 2015

We consider the mass critical two dimensional nonlinear Schrodinger equation (NLS) i∂tu + ∆u + |u| 2 u = 0, t ∈ R, x ∈ R 2. Let Q denote the positive ground state solitary wave satisfying ∆Q − Q + Q…

Finite point blowup for the critical generalized Korteweg-de Vries equation

- Mathematics
- 2021

In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of…

Minimal mass blow-up solutions for the $L^2$-critical NLS with the Delta potential for radial data in one dimension

- Mathematics
- 2021

Abstract. We consider the L-critical nonlinear Schrödinger equation (NLS) with the delta potential i∂tu+ ∂ 2 xu+ μδu + |u| u = 0, t ∈ R, x ∈ R, where μ ∈ R, and δ is the Dirac delta distribution at x…

Stable blow-up dynamics in the L2-critical and L2-supercritical generalized Hartree equation

- Computer Science, MathematicsArXiv
- 2020

The results are similar to the behavior of stable blowup dynamics in the corresponding NLS settings, and one may expect that the form of the nonlinearity in the Schrodinger-type equations is not essential in stable blow-up.

On mass - critical NLS with local and non-local nonlinearities

- Mathematics
- 2022

We consider the following nonlinear Schrödinger equation with the double L-critical nonlinearities iut +∆u+ |u| 4 3u+ μ ( |x| ∗ |u| ) u = 0 in R, where μ > 0 is small enough. Our first goal is to…

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