Blowup for fractional NLS
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Publication:313994
DOI10.1016/j.jfa.2016.08.011zbMath1348.35038arXiv1509.08845OpenAlexW2963006800MaRDI QIDQ313994
Thomas Boulenger, Enno Lenzmann, Dominik Himmelsbach
Publication date: 12 September 2016
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1509.08845
NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- Blowup for fractional NLS
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- Profile decompositions and blowup phenomena of mass critical fractional Schrödinger equations
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Nonlinear fractional Schrödinger equations in one dimension
- The Pohozaev identity for the fractional Laplacian
- On fractional Schrödinger equations in Sobolev spaces
- Fractional powers of closed operators and the semigroups generated by them
- Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
- Semigroups of linear operators and applications to partial differential equations
- Blow-up of \(H^ 1\) solution for the nonlinear Schrödinger equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Blow-up results of virial type for Zakharov equations
- Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
- Dynamical collapse of white dwarfs in Hartree- and Hartree-Fock theory
- Uniqueness of Radial Solutions for the Fractional Laplacian
- On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
- Global Behavior of Finite Energy Solutions to the d-Dimensional Focusing Nonlinear Schrodinger Equation
- Global Well-Posedness for the Fractional Nonlinear Schrödinger Equation
- A Remark on the Blowing-Up of Solutions to the Cauchy Problem for Nonlinear Schrodinger Equations
- Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
- Nonexistence Results for Nonlocal Equations with Critical and Supercritical Nonlinearities
- SOBOLEV INEQUALITIES WITH SYMMETRY
- Blowup for Biharmonic NLS
- Numerical study of fractional nonlinear Schrödinger equations
- Blowup for nonlinear wave equations describing boson stars
- On Blow-up Solutions to the 3D Cubic Nonlinear Schrodinger Equation
- On finite time blow-up for the mass-critical Hartree equations
- Dispersive wave turbulence in one dimension
- Energy concentration of the focusing energy-critical fNLS
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