Publications - Thomas C. Sideris

Acknowledgement: Much of the research contained in these articles has been supported by grants from the National Science Foundation.
  1. Nonexistence of global solutions to semilinear wave equations in high dimension.
    J. Diff. Eq. 52 3 (1984), 378-406.
  2. Global behavior of solutions to nonlinear wave equations in three space dimensions.
    Comm. PDE. 8 12 (1983), 1291-1323.
  3. Formation of singularities in solutions to nonlinear hyperbolic equations.
    Arch. Rat. Mech. Anal. 86 4 (1984), 369-381.
  4. Formation of singularities in three-dimensional compressible fluids.
    Comm. Math. Phys. 101 (1985), 475-485.
  5. (With M. Chipot) An upper bound for the waiting time for nonlinear degenerate parabolic equations.
    Trans. Am. Soc. 288 1 (1985), 423-427.
  6. Global existence of harmonic maps in Minkowski space.
    Comm. Pure Appl. Math. 42 1 (1989), 1-13.
  7. Decay estimates for the three-dimensional inhomogeneous Klein-Gordon equation and applications.
    Comm. PDE. 14 14 (1989), 1421-1455.
  8. (With M. Chipot) On the Abelian Higgs model.
    J. Appl. Math. Phys. 41 (1990), 105-109.
  9. A decay estimate for the three-dimensional Klein-Gordon equation and global existence for nonlinear equations.
    Microlocal Analysis and Nonlinear Waves, M. Beals, R.B. Melrose, and J. Rauch, eds., IMA Volumes in Mathematics and Its Applications. 30 New York: Springer, 1991.
  10. The lifespan of smooth solutions to the three-dimensional compressible Euler equations and the incompressible limit.
    Indiana Math. J. 40 2 (1991), 535-550.
  11. The lifespan of 3D compressible flow.
    Centre de Mathematiques, Ecole Polytechnique. Expose No. V (1991).
  12. (With R. Grauer) Numerical evidence for the finite-time blow up of 3-D incompressible ideal fluids with swirl.
    Phys. Rev. Let. 67 25 (1991), 3511-3514.
  13. (With G. Ponce) Local regularity of nonlinear wave equations in three space dimensions.
    Comm. PDE. 18 1&2 (1993), 169-177.
  14. (With G. Ponce, R. Racke, and E.S. Titi) Global stability of large solutions to the 3D Navier-Stokes equations.
    Comm. Math. Phys. 159 (1994), 329-341.
  15. (With S. Klainerman) On almost global existence for nonrelativistic wave equations in 3D.
    Comm. Pure Appl. Math. 49 (1996), 307-322.
  16. (With R. Grauer) Finite time singularities in ideal fluids with swirl.
    Physica D. 88 (1995), 116-232.
  17. The null condition and global existence of nonlinear elastic waves.
    Inven. Math. 123 (1996), 323-342.
  18. Long-time behavior of nonlinear elastic waves.
    Proc. Conf. on PDE, St. Jean de Monts (1995).
  19. Delayed singularity formation in 2d compressible flow.
    Am. J. Math. 119 2 (1997), 371-422.
  20. (With D. Iftimie and P. Gamblin) On the evolution of compactly supported planar vorticity.
    Comm. PDE. 42 9&10 (1999), 1709-1730. Download postscript version.
  21. Uniform decay estimates for some hyperbolic equations.
    Nonlinear wave equations (Providence, RI, 1998). Contemp. Math. 263. Amer. Math. Soc., Providence, RI, (2000), 185-195.
  22. The null condition and global existence of nonlinear elastic waves.
    Differential equations and mathematical physics (Birmingham, AL, 1999).
    AMS/IP studies in advanced mathematics, 16. Amer. Math. Soc., Providence, RI, (2000), 339-345.
  23. Nonresonance and global existence of prestressed nonlinear elastic waves.
    Annals of Math. 151 (2000), 849-874. Download postscript version.
  24. (With S.-Y. Tu) Global existence for systems of nonlinear wave equations in 3D with multiple speeds.
    SIAM J. Math. Anal. 33 (2001), 477-488. Download.
  25. (With X.-D. Liu) Convergence of the ghost fluid method for elliptic equations with interfaces.
    Math. Comp. 72 (2003), 1731-1746. Download postscript version.
    26. Download pdf version.
  26. (With B. Thomases and D. Wang) Long time behavior of solutions to the 3D compressible Euler equations with damping.
    Comm. PDE. 28 7&8 (2003), 795-816. Download postscript version.
  27. (With B. Thomases) Global existence for 3d incompressible and isotropic elastodynamics via the incompressible limit.
    Comm. Pure Appl. Math. 58 (2005), 750-788. Download postscript version.
  28. Nonlinear hyperbolic systems and elastodynamics.
    Phase Space Analysis of PDEs, Vol. II. Scuole Normale Superiore Pisa (2004), 451-485. Download postscript version.
  29. (With B. Thomases) Local energy decay for solutions of multi-dimensional isotropic symmetric hyperbolic systems.
    J. Hyperbolic Diff. Eq. 3 (2006), 673-690.  Download pdf version.
  30. Dispersive estimates for solutions of multi-dimensional isotropic symmetric hyperbolic systems.
    Advanced Studies in Pure Mathematics, 47 1. Asymptotic Analysis and Singularities. Mathematical Society of Japan (2007), 55-63.
    Download pdf version.
  31. (With B. Thomases) Global existence for three-dimensional incompressible isotropic elastodynamics.
    Comm. Pure Appl. Math. 60 12 (2007), 1707--1730. Download pdf version.

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