## Duke Mathematical Journal

### On the regularity properties of a model problem related to wave maps

#### Article information

Source
Duke Math. J. Volume 87, Number 3 (1997), 553-589.

Dates
First available in Project Euclid: 19 February 2004

http://projecteuclid.org/euclid.dmj/1077242327

Digital Object Identifier
doi:10.1215/S0012-7094-97-08718-4

Mathematical Reviews number (MathSciNet)
MR1446618

Zentralblatt MATH identifier
0878.35075

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B65: Smoothness and regularity of solutions 58G16

#### Citation

Klainerman, Sergiu; Machedon, Matei. On the regularity properties of a model problem related to wave maps. Duke Math. J. 87 (1997), no. 3, 553--589. doi:10.1215/S0012-7094-97-08718-4. http://projecteuclid.org/euclid.dmj/1077242327.

#### References

• [B]1 J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations, Geom. Funct. Anal. 3 (1993), no. 2, 107–156.
• [B]2 J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation, Geom. Funct. Anal. 3 (1993), no. 3, 209–262.
• [CZ] D. Christodoulou and A. Shadi Tahvildar-Zadeh, On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math. 46 (1993), no. 7, 1041–1091.
• [FMS] A. Freire, S. Muller, and M. Struwe, Weak convergence of harmonic maps, preprint.
• [He] F. Hélein, Regularity of weakly harmonic maps from a surface into a manifold with symmetries, Manuscripta Math. 70 (1991), no. 2, 203–218.
• [KPV] C. Kenig, G. Ponce, and L. Vega, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J. 71 (1993), no. 1, 1–21.
• [KM1] S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), no. 9, 1221–1268.
• [KM2] S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Math. J. 81 (1995), no. 1, 99–133 (1996).
• [KM3] S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Internat. Math. Res. Notices (1994), no. 9, 383ff., approx. 7 pp. (electronic).
• [KM4] S. Klainerman and M. Machedon, Remark on Strichartz-type inequalities, Internat. Math. Res. Notices (1996), no. 5, 201–220.
• [KM5] S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J. 74 (1994), no. 1, 19–44.
• [KM6] S. Klainerman and M. Machedon, Finite energy solutions of the Yang-Mills equations in $\bold R\sp 3+1$, Ann. of Math. (2) 142 (1995), no. 1, 39–119.