Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles

DOI10.1007/s11537-011-1108-0zbMath1270.35071OpenAlexW1985201862MaRDI QIDQ1935099

Carlos E. Kenig

Publication date: 30 January 2013

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-011-1108-0

zbMATH Keywords

scatteringglobal existencefinite time blow-upuniversal profileshomogeneous Sobolev spacescritical non-linear dispersive equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Critical exponents in context of PDEs (35B33) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Initial value problems for second-order hyperbolic systems (35L52)

Related Items (1)

Initial value problems for nonlinear dispersive equations at critical regularity

Cites Work

• Radial solutions to energy supercritical wave equations in odd dimensions
• Concentration compactness for critical wave maps
• Small solutions to nonlinear Schrödinger equations
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Nonlinear small data scattering for the wave and Klein-Gordon equation
• Dynamic of threshold solutions for energy-critical NLS
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Energy dispersed large data wave maps in \(2+1\) dimensions
• Regularity of wave-maps in dimension \(2+1\)
• On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model
• Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation
• Convergence of solutions of H-systems or how to blow bubbles
• On a conformally invariant elliptic equation on \(R^ n\)
• Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity
• Space-time decay for solutions of wave equations
• Best constant in Sobolev inequality
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Decay estimates for the critical semilinear wave equation
• On the asymptotic behavior of spherically symmetric wave maps
• Radially symmetric wave maps from \((1+2)\)-dimensional Minkowski space to the sphere
• A Liouville theorem for the critical generalized Korteweg-de Vries equation
• Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
• Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
• On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
• Global and unique weak solutions of nonlinear wave equations
• Generalized Strichartz inequalities for the wave equation
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
• Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Renormalization and blow up for charge one equivariant critical wave maps
• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
• Global regularity of wave maps from \(\mathbb{R}^{2+1}\) to \(H^{2}\). Small energy
• Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrö\-dinger equation for radial data
• On global existence and scattering for the wave maps equation
• Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Dynamics of Threshold Solutions for Energy-Critical Wave Equation
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Local and global results for wave maps I
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
• Space‐time estimates for null forms and the local existence theorem
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• On the cauchy problem for equivariant wave maps
• Equivariant wave maps in two space dimensions
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Global regularity of wave maps. II: Small energy in two dimensions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles