Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

RECENT DEVELOPMENTS IN NONLINEAR HYPERBOLIC PDE

  • Published : 2001.07.01
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Abstract

In this lecture I shall discuss some recent progress in the development of methods for attacking the central questions of the formation and structure of singularities and of global regularity for solutions of the Cauchy problem for nonlinear systems of partial differential equations of hyperbolic type. Applications to the Einstein equations of general relativity and to the equations of compressible fluid flow shall be particularly emphasized and detailed.

Keywords

References

  1. Princeton Mathematical Series v.41 The global nonlinear stability of the Minkowski space D. Christodoulou;S. Klainerman
  2. Stability of Minkowski space-time Surveys in Differential Geometry, V: Essays on Einstein Manifolds D. Christodolou;McKenzie Wang(ed.);Claude LeBrun(ed.)
  3. AMS/IP Stud. Adv. Math. v.16 The initial value problem in the large and spacetime singularities
  4. Comm. Math. Phys. v.14 Global aspects of the Cauchy problem in general relativity Y. Choquet-Bruhat;R. P. Geroch
  5. Acta Math. v.88 Theoreme d' existence pour certain systemes d'equations aux derivees partielles nonlinaires Y. Choquet-Bruhat
  6. Proc. Roy. Soc. Lond. v.A312 The sigularities of gravitational collapse and cosmology S. W. Hawking;R. Penrose
  7. Fluid Mechanics(2nd edition) L. D. Landau;E. M. Lifschitz
  8. Phys. Rev. Lett. v.14 Gravitational collapse and space-time singularities R. Penrose
  9. Rivista del Nuovo Cimento v.1 Gravitational collapse: the role of general relativity
  10. General Relativity Singularities and time-asymmetry S. W. Hawking(ed.);W. Israel(ed.)
  11. Comm. Math. Phys. v.101 The formation of singularities in three-dimensional compressible fluids T. Sideris