Maria Schonbek Publications

  1. Boundary value problems for the Fitzhugh-Nagumo equations. Journal of Differential Equations 30 (1), pp. 119-47, (1978).
  2. Some results on the Fitzhugh-Nagumo equations, Research Notes in Mathematics, No. 14, Editors: W. E. Fitzgibbon and H. F. Walker, (Pitman, 1977).
  3. Decay of solutions to parabolic conservation laws, Communications in Partial Differential Equations 7 (1), pp.449-73, (1980).
  4. Decay of solutions to the Korteweg-deVries-Burger equation and to parabolic conservation laws, Nonlinear Partial Differential Equations in Engineering and Applied Science, vol. 54, Editors: R. L. Sternberg, A. Kalinowski and J. Papadakis, (Marcel Dekker, 1980). 10. L2 decay for weak solutions of the Navier-Stokes equations, Archive of Rational Mechanics 88 (3), pp. 209-22, (1985).
  5. Apriori estimates of higher order derivatives of solutions of the Fitzhugh-Nagumo equations, Journal of Mathematical Applications 82 (2), pp. 553-65, (1981).
  6. Existence of solutions to the Boussinesq system of equations, Journal of Differential Equations 42 (3), (1981), pp. 325-51.
  7. Convergence of solutions to nonlinear dispersion equations, Communications in Partial Differential Equations 7 (8), (1982), pp. 959-1000.
  8. Existence of solution to singular conservation laws, SIAM Journal of Mathematical Analysis 15 (6), pp. 1125-39, (1984).
  9. Second order conservative schemes and the entropy condition, Mathematics of Computations Vol. 10, No. 169, pp. 31-38, (Jan. 1985).
  10. L^2 decay for weak solutions of the Navier-Stokes equations, Archive of Rational Mechanics 88 (3), pp. 209-22, (1985).
  11. Some results on the traveling wave solutions of the Korteweg-deVries-Burger equation, (with J. Bona) Royal Society of Edinburgh, 101A, pp. 207-26, (1985).
  12. Uniform decay rates for parabolic conservation laws, Journal of Nonlinear Analysis Vol. 10, No. 9, pp. 943-56, (1986).
  13. Large time behavior of solutions to the Navier-Stokes equations, Communications in Partial Differential Equations 11 (7), pp. 733-763, (1986).
  14. Applications to the theory of compensated compactness, Oscillation theory, computation, and methods of compensated compactness (Minneapolis, Minn, 1985), 289-294 (IMA) Vol. Math. Appl2, Springer, New York, (1986).
  15. Nonlinear geometric optics and conservation laws, Proceedings of the Symposium Year on material instabilities in continuous mechanics. Heriot-Watt University. Edited by John Ball, (1986).
  16. Some aspects on compressible and incompressible gas dynamics, Proceedings of the Conference on Nonlinear Partial Differential Equations and Applications at the University Palazzo dei Gesuiti, L'Aquila, Italy, (1986).
  17. A canonical system of integro-differential equations arising in resonant wave asymptotics, (with A. Majda and R. Rosales) Studies in Applied Mathematics, (79), no. 3 205-262, (1988).
  18. Asymptotic properties for long waves which incorporate dissipation, (with J. Bona and C. Amick), Journal of Differential Equations 81, no 1, 1-49, (1989).
  19. Lower bounds of decay rates for the solutions to Navier-Stokes equations, Journal of the American Mathematical Society, (July 1991).
  20. Asymptotic behavior of solutions to the three dimensional Navier-Stokes equations, Indiana University Journal, Vol. 41, no. 2 (1992).
  21. Some results on the asymptotic behavior of solutions to Navier Stokes. Proceedings of the Oberwolfach Conference on Navier-Stokes equations, Springer-Verlag (NOTE: these proceedings are reviewed), (1991).
  22. Models for propagation of bores I. Two-dimensional theory. (Previously titled: Long wave models with initial data corresponding to bore propagation), (with J. Bona and S. Rajopadhye) Differential Integral Equations, 7, no.3-4 699-734, (1994).
  23. Large-time behavior of solutions to the Navier-Stokes equations in H^m spaces, Comm. in P.D.E, 20 (1& 2), pp. 103-117 (1995).
  24. Estimates for the pressure and the Fourier transform of solutions and derivatives to the Navier-Stokes equations. Indiana Math Journal, vol. 43 #2, (1994).
  25. The Fourier splitting method, Advances in Geometric Analysis and Continuum Mechanics, (269-274), Internatl. Press, Cambridge, Ma. (1995).
  26. Asymptotic behavior of solutions to the Korteweg de Vries-Burger System (with S. Rajopadhye, Analyse Nonlineare, vol. 12, no.44, pp. 425-457 (1995).
  27. Decay results for Solutions to the Magneto Hydrodynamics equations, (with T.P. Schonbek and E. Suli) Mathematical Analysis of Phenomena in Fluids and Plasma Dynamics. Editors: K. Asano, A. Tani, S. Ukai. RIMS Kokyuroku 914, 98-102, (1995).
  28. Large-time behavior of solutions to the Magneto-Hydrodynamics equations (with T. P. Schonbek and E. Süli). Mathematische Annalen, 304, no.4 717-756, (1996).
  29. On the decay of higher order norms of the solutions of Navier-Stokes equations, (joint with M. Wiegner) Proc. Royal Society of Edinburgh Sect. A 126, no.3, 677-685, (1996).
  30. Asymptotic behavior of solutions to the Navier-Stokes equations with slowly decaying external force, (with S. Rajopadhye and T. Ogawa), J. Functional Analysis 144, no. 2. 325-358, (1997).
  31. Decay of Solutions to non-oscillating Magneto Hydrodynamics equations. Proceedings of Oberwolfach Conference on Navier Stokes (Springer Verlag Proceedings), Theory of the Navier-Stokes Equations. Editors Heywood, Masuda, Rautmann, Solonikov. Series on advances in Math for Applied Sciences- Vol. 47 (1998). (NOTE: these proceedings are reviewed).
  32. On the possible singular solutions to the Navier-Stokes equations (joint with Malek, Necas, Pocorny), Mathematische Nachrichten, 199, (1999) 97-114.
  33. Asymptotic decay to a generalized Boussinesq System (with S. Rajopadhye and M. Wiegner), J. of Dynamics and Differential Equations vol. 11, #4, (1999).
  34. Energy decay of solutions of the Planetary geostrophic equations, joint with G.K. Vallis, J. Math. Ann. and Appl., 234, 457-481 (1999).
  35. On the boundedness and decay of moments of solutions to the Navier-Stokes equations, joint with T.P. Schonbek, Advances in Differential Equations, Vol. 5, #7-9, July-September (2000).
  36. Strong solutions to the incompressible Navier-Stokes equations in the half space. Joint with M. Cannone and F. Planchon. Comm. in PDE, 25 (5&6), 903-924, (2000).
  37. On the Decay of Solutions to the Navier-Stokes Equations. Applied Nonlinear Analysis, Editors: A. Sequeira, H. Beirao da Vega, J. H. Videman, Kluwer Academic/ Plenum Publisher. (NOTE: The papers in this book are reviewed). (1999).
  38. Pointwise decay of solutions and higher derivatives to Navier-Stokes equations, (joint with Amrouche, Girault and T. Schonbek), SIAM Journal of Analysis, Vol. 31, (4), (2000).
  39. Geodesic flow on Diffeomorphism of the Circle, Grassmanians and the Geometry of Periodic KdV equations, joint with A.Todorov, J. Zubelli, Adv. Theor. Math. Physics, 4,1027-1090, (2000).
  40. Total variation decay of solutions to the Navier-Stokes equations. Methods and Applications of Analysis, Vol7, No 3,555-564, (2000).
  41. Decay of the total variation and Hardy norms to parabolic conservation laws, joint with SŸli, Nonlinear Analysis, 45, 515-528, (2001).
  42. Nonexistence of Singular Pseudo-self-similar Solutions of the Navier-Stokes System, joint with J. Miller, M. O'Leary, Mathematiche Annalen, 319, 809-815, (2001).
  43. On Optimal Decay Rates for Weak Solutions to the Navier-Stokes Equations in IR^n, joint with T. Miyakawa. Mathematica Bohemica, Vol. 126, No 2, 257-263, (2001).
  44. On zero mass solutions of viscous conservation laws, joint with G. Karch.  Comm. in PDE,27, (2002) no.9-10.
  45. Asymptotic Behavior to Dissipative Quasi-Geostrophic equations, joint with Tomas Schonbek, SIAM J. Math, Anal}. 35(2003) no2, 357-375.
  46. FitzHugh-Nagumo Revisited: Types of bifurcations, periodical forcing and stability regions by a Lyapunov functional. Joint with T. Kostova and R. Ravindran.
     International journal of bifurcation and chaos, vol 14, no 3 (2004) 913-925.
  47. Moments and Lower bounds in the far-field of solutions to Quasi-Geostrophic flows.  Joint with Tomas Schonbek. Journal of Discrete and Continuous Dynamical Systems Series A , volumen 13, no 5 , December 2005.
  48. Asymptotic behavior of solutions to viscous conservation lawswith slowly varying external forces.  Mathematischen Annalen. Volume 336, Number 3,  November, 2006.
  49. Decay to weak solutions of the 2D dissipative Quasi-geostrophic equations with supercritical exponents. Joint with C. Niche. Communications in Math Physics. Volume 276, Number 1. November, 2007.
  50. Non-uniform deay for MHD equations with and without magnetic diffusion. Joint with R. Agapito.   Comm in PDE. Volume 32, Issue 11, 2007, Pages 1791 – 1812.
  51. On existence and asymptotic behavior of the Viscous Camassa-Holms equations.  Joint with C. Bjorland. Ann. Inst. H. Poincaré Anal. Non Linaire 25 (2008), no. 5, 907-936
  52. Poincaré's inequality and diffusive equations.  Joint with C. Bjorland. Adv. Differential Equations 14 (2009), no. 3-4, 241-260.
  53. Decay and existence of polymeric flows. Vol 41, issue 2, SIAM Journal on Mathematical Analysis. 2009.
  54. Existence and stability of steady-state solutions with finite energy for the Navier-Stokes equations in the whole space. Joint with C. Bjorland, Nonlinearity 22 (2009) 1615-1637.
  55. Lp-solutions of the steady-state Navier-Stokes equations with Rough External Forces. Joint with C. Bjorland, L. Brandolese, D. Iftimie. Comm. Partial Differential Equations 36 (2011), no. 2, 216-246.
  56. Norm inflation for incompressible magneto-hydrodynamic system Joint with M. Dai and J. Qing. Advances for Differential equations, Volume 16, Numbers 7-8, July/August 2011.
  57. Large time decay and growth for solutions of a viscous Boussinesq system. Joint with L Brandolese. Transactions of the American Mathematical society. Vol. 364, Number 10. 5057-5090. October 2012
  58. Non existence of pseudo-self-similar solutions to incompressible Euler equa- tions Acta Math Sci, vol 31, issue 6, (2011) 2305-2312.
  59. Navier-Stokes space time decay revisited. Journal GAKUTO International Series Mathematical sciences and applications. Volume 35, 2011.
  60. On the Oberbeck-Boussinesq approximation on unbounded domains. Joint with E. Fereisl. (Accepted for publication, the papers in the Abel Proceedings are reviewed).
  61. Decay Rates for a class of Diffusive-dominated Interaction Equations. Joint with J.A. Can L~Cizo and J. A. Carrillo. Journal of Mathematical analysis and applications. Volume 389, Issue 1, Pages 541557. May 2012
  62. Regularity of solutions to the liquid crystals systems in R2 and R3. Joint with M. Dai and J. Qing. Nonlinearity 25 513, 2012.
  63. Asymptotic Behavior of Solutions to Liquid Crystal Systems in $\mathbb{R}^3$ Joint with M. Dai and J. Qing. Communications in PDE, Volume 37, Issue 12, January 2012, pages 2138-2164.
  64. Classical Solutions for a Fokker-Planck equation arising in Computational Neuroscience. Joint with J.A. Carrillo and M. del M. Gonzalez, Maria Gualdani ( Accepted in Communications in PDE).
  65. Asymptotic Behavior of Solutions to the Liquid Crystal Systems in H^m(R^3) (submitted).


  1. Problems related to solutions to the Navier-Stokes equations. Fachbereich Mathematik, Bericht 203, Nov. 1998.