Existence de solutions explosives dans l’espace d’énergie pour l’équation de Korteweg–de Vries généralisée critique

Yvan Martel; Frank Merle

Séminaire Équations aux dérivées partielles (2001-2002)

  • page 1-9

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Martel, Yvan, and Merle, Frank. "Existence de solutions explosives dans l’espace d’énergie pour l’équation de Korteweg–de Vries généralisée critique." Séminaire Équations aux dérivées partielles (2001-2002): 1-9. <http://eudml.org/doc/11042>.

@article{Martel2001-2002,
author = {Martel, Yvan, Merle, Frank},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Existence de solutions explosives dans l’espace d’énergie pour l’équation de Korteweg–de Vries généralisée critique},
url = {http://eudml.org/doc/11042},
year = {2001-2002},
}

TY - JOUR
AU - Martel, Yvan
AU - Merle, Frank
TI - Existence de solutions explosives dans l’espace d’énergie pour l’équation de Korteweg–de Vries généralisée critique
JO - Séminaire Équations aux dérivées partielles
PY - 2001-2002
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 9
LA - eng
UR - http://eudml.org/doc/11042
ER -

References

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  2. D.B. Dix and W.R. McKinney, Numerical computations of self-similar blow up solutions of the generalized Korteweg-de Vries equation, Diff. Int. Eq., 11 (1998), 679—723. Zbl1007.65061MR1664756
  3. W. Eckhaus and P. Schuur, The emergence of solitons of the Korteweg–de Vries equation from arbitrary initial conditions, Math. Meth. Appl. Sci. 5 (1983), 97—116. Zbl0518.35074MR690898
  4. C.E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg–de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46, (1993) 527—620. Zbl0808.35128MR1211741
  5. D.J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. 539, (1895) 422—443. Zbl26.0881.02
  6. G.L. Lamb Jr., Element of soliton theory (John Wiley & Sons, New York 1980). Zbl0445.35001MR591458
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  9. Y. Martel and F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157, (2001) 219—254. Zbl0981.35073MR1826966
  10. Y. Martel and F. Merle, Stability of the blow up profile and lower bounds on the blow up rate for the critical generalized KdV equation, Ann. of Math. 155, (2002) 235—280. Zbl1005.35081MR1888800
  11. Y. Martel and F. Merle, Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equation, à paraître dans J. Amer. Math. Soc. Zbl0996.35064MR1896235
  12. Y. Martel, F. Merle and Tai–Peng Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, préprint. Zbl1017.35098MR1946336
  13. F. Merle, Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations, Proceeding of the International Congress of Mathematicians, (Berlin, 1998), Doc. Math. J. DMV. Zbl0896.35123MR1648140
  14. F. Merle, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, J. Amer. Math. Soc. 14, (2001) 555—578. Zbl0970.35128MR1824989
  15. F. Merle and P. Raphael, Blowup dynamic and upper bound on the blowup rate for the critical nonlinear Schrödinger equation, préprint. Zbl1185.35263
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  17. M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983), 567—576. Zbl0527.35023MR691044

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