Geodesic
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations
Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 57-66.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We review qualitative properties of solutions of critical nonlinear Schrödinger equation $$iu_t= -\Delta u-| u|^{p-1}u, \quad u(0)= u_0,$$ and Zakharov equations $$ iu_t= -\Delta u+nu, \quad n_t= -\nabla\cdot v, \quad \frac{1}{c_0^2} v_t= -\nabla(n+| u|^2),$$ which develop a singularity in finite time.
Classification : 35Q55, 35B40, 35J60
Keywords: Zakharov equations, formation of singularities in time, Hamiltonian systems, nonlinear Schrödinger equation 
@article{DOCMA_1998__S9__a72,
     author = {Merle, Frank},
     title = {Blow-up phenomena for critical nonlinear {Schr\"odinger} and {Zakharov} equations},
     journal = {Documenta mathematica},
     pages = {57--66},
     publisher = {mathdoc},
     volume = {ICM Berlin 1998, Vol. III},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a72/}
}
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Merle, Frank. Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations. Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 57-66. http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a72/