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LOCAL EXISTENCE FOR SEMILINEAR WAVE EQUATIONS AND APPLICATIONS TO YANG–MILLS EQUATIONS

YUNG-FU FANG

Department of Mathematics, Cheng Kung University, Tainan 701 Taiwan, R.O.C.

https://doi.org/10.1142/S0219891605000373Cited by:0 (Source: Crossref)

Abstract

In this work we are concerned with a local existence of certain semi-linear wave equations for which the initial data has minimal regularity. Assuming the initial data are in H^1+∊ and H^∊ for any ∊ > 0, we prove a local result by using a fixed point argument, the main ingredient being an a priori estimate for the quadratic nonlinear term uDu. The technique applies to the Yang–Mills equations in the Lorentz gauge.

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References

F. M. Christ and M. I. Weinstein, J. Funct. Anal. 100, 87 (1991). Crossref, Web of Science, Google Scholar
R. Coifman and Y. Meyer, Astériques 57, (1978). Google Scholar
D. Eardley and V. Moncrief, Commun. Math. Phys. 83, 171 (1982). Crossref, Web of Science, Google Scholar
D. Gilbarg and N. Trudinger , Elliptic P.D.E. of Second Order ( Springer-Verlag , Germany , 1983 ) . Crossref, Google Scholar
J. Ginibre and G. Velo, Commun. Math. Phys. 82, 1 (1981). Crossref, Web of Science, Google Scholar
R. T. Glassey and W. Strauss, Commun. Math. Phys. 65, 1 (1979). Crossref, Web of Science, Google Scholar
R. T. Glassey and W. Strauss, Commun. Math. Phys. 81, 171 (1981). Crossref, Web of Science, Google Scholar
T. Kato and G. Ponce, Comm. Pure Appl. Math. 41, 891 (1988). Crossref, Web of Science, Google Scholar
S. Klainerman, The null conditions and global existence to nonlinear wave equations, in Lectures in Applied Math., ed. B. Nicolaenko 23 (1986) . Google Scholar
S. Klainerman and M. Machedon, Duke Math. J. 74, 19 (1994). Crossref, Web of Science, Google Scholar
S. Klainerman and M. Machedon, Comm. Pure Appl. Math. 46, 1221 (1993). Crossref, Web of Science, Google Scholar
S. Klainerman and M. Machedon, Ann. of Math. 142, 39 (1995). Crossref, Web of Science, Google Scholar
H. Lindblad, Duke Math. J. 72, 503 (1993). Crossref, Web of Science, Google Scholar
H. Lindblad, Amer. J. Math. 118, 1 (1996). Crossref, Web of Science, Google Scholar
G. Ponce and T. C. Sideris, Comm. PDE 18, 169 (1993). Crossref, Web of Science, Google Scholar
P. P. S. Schirmer, Global Existence for Spherically Symmetric Yang–Mills Fields on 3+1 Space–Time Dimensions, PhD dissertation, New York University (1990) . Google Scholar
I. Segal, J. Funct Anal. 33, 175 (1979). Crossref, Web of Science, Google Scholar
E. M. Stein , Singular Integral and Differentiability Properties of Functions ( Princeton University Press , Princeton, New Jersey , 1970 ) . Google Scholar
E. M. Stein , Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals ( Princeton University Press , Princeton, New Jersey , 1993 ) . Google Scholar
W. A. Strauss , Nonlinear Wave Equations 73 ( CBMS AMS Providence , Rhode Island , 1989 ) . Google Scholar

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LOCAL EXISTENCE FOR SEMILINEAR WAVE EQUATIONS AND APPLICATIONS TO YANG–MILLS EQUATIONS

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