A semilinear Dirac equation in Hs(R3) for s > 1

SIAM Journal on Mathematical Analysis

Volumn 28, Issue 2, 1997, Pages 338-362

  Escobedo, M ^a   Vega, L ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Dirac equation; Sobolev spaces; Well posedness

Indexed keywords

EID: 0031528934     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095283017     Document Type: Article

References (18)

1. M. BALABANE, T. CAZENAVE, A. DOUADY, AND F. MERLE, Existence of excited states for a nonlinear Dirac field, Comm. Math. Phys., 119 (1988), pp. 153-176.
2. q estimates for the wave equation, Math. Z., 145 (1975), pp. 251-254.
3. T. CAZENAVE AND L. VAZQUEZ, Existence of localized solutions for a classical nonlinear Dirac field, Comm. Math. Phys., 105 (1986), pp. 35-47.
4. s, Nonlinear Anal., 14 (1990), pp. 807-836.
5. s for the massive nonlinear Dirac equations in three space dimensions, Boll. Un. Mat. Ital. B(7), 1 (1987), pp. 861-874.
6. M-valued functions, Rev. Mat. Univ. Comput. Madrid, 1 (1988), pp. 127-144.
7. M. J. ESTEBAN AND E. SERE, Stationary states of the nonlinear Dirac equation: A variational approach, Preprint 9321, CEREMADE, Université de Paris, Dauphine, Paris, 1993; Comm. Math. Phys., 171 (1995), pp. 323-350.
8. M. J. ESTEBAN AND E. SERE, Stationary states of the nonlinear Dirac equation: A variational approach, Preprint 9321, CEREMADE, Université de Paris, Dauphine, Paris, 1993; Comm. Math. Phys., 171 (1995), pp. 323-350.
9. R. FINKELSTEIN, R. LELEVIER, AND M. RUDERMAN, Nonlinear Spinor fields, Phys. Rev., 83 (1951), pp. 326-332.
10. 2 pour une équation de Dirac non linéaire, Portugal. Math., 46 (1989), pp. 553-565 (supplement).
11. B. NAJMAN, The nonrelativistic limit of the nonlinear Dirac equation, Ann. Inst. H. Poincaré Anal. Non Lineaire, 9 (1992), pp. 3-12.
12. G. PONCE AND T. C. SIDERIS, Local regularity of nonlinear wave equations in three space dimensions, Comm. Partial Differential Equations, 18 (1993), pp. 169-177.
13. A. F. RAÑADA, Classical nonlinear Dirac field models of extended particles, in Quantum Theory, Groups, Fields and Particles, D. Reidel, Amsterdam, 1982.
14. M. REED, Abstract Non-Linear Wave Equations, Lecture Notes in Math. 507, Springer-Verlag, Berlin, 1976.
15. M. SOLER, Classical, stable nonlinear spinor field with positive rest energy, Phys. Rev. D, 1 (1970), pp. 2766-2769.
16. H. TRIEBEL, Theory of Function Spaces, Birkhäuser-Verlag, Basel, Switzerland, 1983.
17. M. WAKANO, Intensely localized solutions of the classical Dirac-Maxwell field equations, Progr. Theoret. Phys., 35 (1966), pp. 1117-1141.
18. p, Indiana Univ. Math J., 29 (1980), pp. 79-102.