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Merle, Frank

  1. Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation
    2006/10/26 by Carlos E. Kenig, Kenig, Carlos E., Merle, Frank · 8 citations
    Arts and Humanities · Mathematics · #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Crime and Detective Fiction Studies #FOS: Mathematics #Navier-Stokes equation solutions
  2. Dynamic of threshold solutions for energy-critical NLS
    2007/10/31 by Thomas Duyckaerts, Duyckaerts, Thomas, Merle, Frank · 4 citations
    Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations
  3. Scattering for H1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions
    2007/12/11 by Kenig, Carlos E., Merle, Frank · 4 citations
    #35Q55 #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics
  4. Classification of radial solutions of the focusing, energy-critical wave equation
    2012/03/30 by Duyckaerts, Thomas, Kenig, Carlos, Merle, Frank · 4 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  5. Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations
    2009/05/04 by Cote, Raphael, Martel, Yvan, Merle, Frank · 4 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  6. On blow up for the energy super critical defocusing non linear Schrödinger equations
    2019/12/23 by Merle, Frank, Raphael, Pierre, Rodnianski, Igor +1 · 4 citations
    #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics
  7. Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation
    2009/10/14 by Duyckaerts, Thomas, Kenig, Carlos, Merle, Frank · 3 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  8. Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations
    2001/12/07 by Yvan Martel, Frank Merle, Martel, Yvan +4 · 3 citations
    Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AP
  9. Soliton resolution for the radial critical wave equation in all odd space dimensions
    2019/12/16 by Duyckaerts, Thomas, Kenig, Carlos E., Merle, Frank · 4 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  10. Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation
    2008/07/18 by Duyckaerts, Thomas, Merle, Frank · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  11. Scattering for radial, bounded solutions of focusing supercritical wave equations
    2012/08/10 by Duyckaerts, Thomas, Kenig, Carlos, Merle, Frank · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  12. Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions
    2013/09/30 by Merle, Frank, Zaag, Hatem · 2 citations
    #35B40 #35B44 #35L05 #35L67 #35L71 #Analysis of PDEs (math.AP) #FOS: Mathematics
  13. Type II blow up for the energy supercritical NLS
    2014/07/05 by Merle, Frank, Raphael, Pierre, Rodnianski, Igor · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  14. Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications
    2008/10/27 by Carlos E. Kenig, Frank Merle, Kenig, Carlos E. +1 · 2 citations
    Mathematics · Physics and Astronomy · #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
  15. Solutions of the focusing nonradial critical wave equation with the compactness property
    2014/02/03 by Duyckaerts, Thomas, Kenig, Carlos E., Merle, Frank · 2 citations
    #35B99 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35L05. Secondary: 35L71
  16. Soliton resolution for the radial quadratic wave equation in six space dimensions
    2022/01/05 by Collot, Charles, Duyckaerts, Thomas, Kenig, Carlos +1 · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  17. Description of two soliton collision for the quartic gKdV equation
    2007/09/17 by Martel, Yvan, Merle, Frank · 2 citations
    #35B40 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics
  18. Dynamic of threshold solutions for energy-critical wave equation
    2007/10/31 by Thomas Duyckaerts, Duyckaerts, Thomas, Frank Merle +1 · 1 citation
    Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
  19. Stable self similar blow up dynamics for slightly L2 supercritical NLS equations
    2009/07/23 by Merle, Frank, Raphael, Pierre, Szeftel, Jeremie · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  20. Inelastic interaction of nearly equal solitons for the quartic gKdV equation
    2009/10/16 by Martel, Yvan, Merle, Frank · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  21. The instability of Bourgain-Wang solutions for the L2 critical NLS
    2010/10/25 by Merle, Frank, Raphael, Pierre, Szeftel, Jeremie · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  22. Maximizers for the Strichartz norm for small solutions of mass-critical NLS
    2010/07/02 by Duyckaerts, Thomas, Merle, Frank, Roudenko, Svetlana · 1 citation
    #35B45 #35B50 #35P25 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics
  23. Blow up for the critical gKdV equation II: minimal mass dynamics
    2012/04/20 by Martel, Yvan, Merle, Frank, Raphael, Pierre · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  24. Profiles of bounded radial solutions of the focusing, energy-critical wave equation
    2012/01/24 by Duyckaerts, Thomas, Kenig, Carlos, Merle, Frank · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  25. Blow up for the critical gKdV equation III: exotic regimes
    2012/09/12 by Martel, Yvan, Merle, Frank, Raphael, Pierre · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  26. Universality of blow up profile for small blow up solutions to the\n energy critical wave map equation
    2016/12/14 by Thomas Duyckaerts, Duyckaerts, Thomas, Hao Jia +5 · 1 citation
    Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
  27. Profiles for bounded solutions of dispersive equations, with\n applications to energy-critical wave and Schr "odinger equations
    2013/11/04 by Thomas Duyckaerts, Duyckaerts, Thomas, Carlos E. Kenig +3 · 1 citation
    Mathematics · Physics and Astronomy · #35B40 #35L05 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
  28. Soliton resolution along a sequence of times for the focusing energy critical wave equation
    2016/01/08 by Duyckaerts, Thomas, Jia, Hao, Kenig, Carlos +1 · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  29. On the implosion of a three dimensional compressible fluid
    2019/12/23 by Frank Merle, Pierre Raphaël, Merle, Frank +5 · 1 citation
    Earth and Planetary Sciences · Engineering · Mathematics · #35Q35 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions