Igor Kukavica (Publications)

Research Interests

Partial differential equations

Nonlinear dynamics/Navier-Stokes Equations

Publications; some links (such as Science Direct) require subscriptions

68. (with A. Tuffaha), Solutions to a fluid-structure interaction free boundary problem, Discrete Contin. Dyn. Syst. 32 (2012), no. 4, 1355–1389. published version  pdf

67. (with V. Vicol), On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations, Nonlinearity 4 (2011), 765-796. published version  pdf

66. (with A. Tuffaha and M. Ziane), Strong solutions to a Navier-Stokes-Lame' system on a domain with a non-flat boundary, Nonlinearity 24 (2011), 159-176. published version  pdf

65. (with E. Reis), Asymptotic expansion for solutions of the Navier-Stokes equations with potential forces, J. Diff. Eq. 250 (2011), 607-622. published version  pdf

64. (with R. Temam, V. Vicol, and M. Ziane), Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain, J. Diff. Eq. 250 (2011), 1719-1746. published version  pdf

63. Partial regularity for the Navier-Stokes equations with a force in a Morrey space, J. Math. Anal. Appl. 374 (2011), 573-584. published version  pdf

62. (with V. Vicol), Domain of analyticity for solutions of the three-dimensional Euler equations in half space, Discrete Contin. Dynam. Systems 29 (2011), 285-303. published version  pdf

61. (with R. Temam, V. Vicol, and M. Ziane), Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain, C. R. Math. Acad. Sci. Paris 348 (2010), 639-645. published version

60. (with M. Ignatova), Unique continuation and complexity of solutions to parabolic partial differential equations with Gevrey coefficients, Adv. Diff. Eq. 15 (2010), 953-975. pdf

59. On regularity for the Navier-Stokes equations in Morrey spaces, Discrete Contin. Dynam. Systems 26 (2010), 1319-1328. published version

58. (with A. Tuffaha and M. Ziane), Strong solutions to a fluid structure interaction system, Adv. Diff. Eq. 15 (2010), 231-254. pdf

57. Partial regularity results for solutions of the Navier-Stokes system, J. Rodrigo and J.C. Robinson editors, Proceedings of the workshop on ``Partial differential equations and fluid mechanics,'' Warwick, 2009. pdf

56. The fractal dimension of the singular set for solutions of the Navier-Stokes system, Nonlinearity 22 (2009), 2889-2900. published version  pdf

55. (with A. Tuffaha and M. Ziane), Strong solutions to a nonlinear fluid structure interaction system, J. Diff. Eq. 247 (2009), 1452-1478. published version  pdf

54. On the weighted decay for solutions of the Navier-Stokes system, Nonlinear Anal. 70 (2009), 2466-2470. published version  pdf

53. (with Vlad Vicol), On the radius of analyticity of solutions to the three-dimensional Euler equations, Proc. Amer. Math. Soc. 137 (2008), 669-677. published version  pdf

52. (with M. Ziane), Uniform gradient bounds for the primitive equations of the ocean, Differential Integral Equations 21 (2008), 837-849. pdf  pdf

51. Regularity for the Navier-Stokes equations with a solution in a Morrey space, Indiana Univ. Math. J. 57 (2008), 2843-2860. published version  pdf

50. (with Vlad Vicol), On local uniqueness of weak solutions to the Navier-Stokes system with $BMO^-1$ initial datum, J. Dynam. Differential Equations 20 (2008), 719-732. published version  pdf

49. On partial regularity for the Navier-Stokes equations, Discrete Contin. Dynam. Systems 21 (2008), 717-728. published version  pdf

48. (with M. Ziane), On the Regularity of the primitive equations of the ocean, Nonlinearity 20 (2007), 2739-2753. published version  pdf

47. (with M. Ziane), The regularity of solutions of the primitive equations of the ocean in space dimension three, C. R. Math. Acad. Sci. Paris 345 (2007), 257-260. published version  pdf

46. (with M. Ziane) Navier-Stokes equation with regularity in one direction, J. Math. Phys. 48 (2007), 10pp. published version

45. (with J.J. Torres) Weighted $L^p$ decay for solutions of the Navier-Stokes equations, Comm. Partial Differential Equations, 32 (2007), 819­831. published version

44. Log-log convexity and backward uniqueness, Proc. Amer. Math. Soc. 135 (2007), 2415-2421. published version

43. (with M. Ziane) On the regularity of the Navier-Stokes equation in a thin periodic domain, J. Differential Equations 234 (2007), 485-506. published version

42. (with M. Ziane) Sur la re'gularite' des e'quations de Navier-Stokes dans un domaine mince pe'riodique, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 97-102. published version

41. (with M. Ziane) Re'gularite' conditionnelle des e'quations de Navier-Stokes, C. R. Acad. Sci. Paris, Ser. I 343 (2006), 31-36. published version

40. Role of the pressure for validity of the energy equality for solutions of the Navier-Stokes equation, J. Dynamics Differential Equations 18 (2006), 461-482. published version

39. (with M. Ziane) Regularity of the Navier-Stokes equation in a thin periodic domain with large data, Discrete Contin. Dyn. Syst. 16 (2006), 67-86. published version

38. Pressure integrability conditions for uniqueness of mild solutions of the Navier-Stokes system, J. Diff. Eq. 223 (2006), 427-441. published version

37. (with M. Ziane) One component regularity for the Navier-Stokes equation, Nonlinearity 19 (2006), 453-469. published version

36. (with J.J. Torres) Weighted bounds for velocity and vorticity for the Navier-Stokes equations, Nonlinearity 19 (2006), 293-303. published version

35. On Fourier parameterization of global attractors for equations in one space dimension, Discrete Contin. Dyn. Syst. 13 (2005), 553-560. published version

34. (with M. Malcok) Backward behavior of solutions of the Kuramoto-Sivashinsky equation, J. Math. Anal. Appl. 307 (2005), no. 2, 455-464. published version

33. (with J. Robinson) Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem, Phys. D 196 (2004), no. 1-2, 45-66. published version

32. Backward uniqueness for solutions of linear parabolic equations, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1755-1760 published version

31. Spatial complexity of solutions of higher order partial differential equations, Nonlinearity 17 (2004), no. 2, 459-476. published version

30. Fourier parameterization of attractors for dissipative equations in one space dimension. Special issue dedicated to Victor A. Pliss on the occasion of his 70th birthday, J. Dynam. Differential Equations 15 (2003), no. 2-3, 473-484. published version

29. On local uniqueness of solutions of the Navier-Stokes equations with bounded initial data, J. Diff. Eq 194 (2003), 39-50. published version (pdf)

28. Length of vorticity nodal sets for solutions of the Navier-Stokes system, Comm. PDE 28 (2003), 771-793. published version (pdf)

27. (with Z. Grujic) A remark on time-analyticity for the Kuramoto-Sivashinsky equation, Nonlinear Analysis 52 (2003), 69-78. published version (pdf)

26. Space-time decay for solutions of the Navier-Stokes equations. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000), Indiana Univ. Math. J. 50 (2001), Special Issue, 205-222. published version (pdf)

25. Interior gradient bounds for the 2D Navier-Stokes system, Discrete Contin. Dynam. Systems 7 (2001), no. 4, 873-882 published version (pdf)

24. (with P. Friz and J. Robinson) Nodal parametrisation of analytic attractors, Discrete Contin. Dynam. Systems 7 (2001), no. 3, 643-657 published version (pdf)

23. (with C. Foias, M.S. Jolly, and E.S. Titi) The Lorenz equation as a metaphor for the Navier-Stokes equations, Discrete Contin. Dynam. Systems 7 (2001), 403-429. published version (pdf)

22. Quantitative Uniqueness and Vortex Degree Estimates for Solutions of the Ginzburg-Landau Equation, Electron. J. Differential Equations 2000 (2000), 1-15 (electronic). (pdf)

21. A ladder inequality for the Navier-Stokes equation, Nonlinearity 13 (2000), 639-652. published version (pdf)

20. On the dissipative scale for the Navier-Stokes equation, Indiana Univ. Math. J. 48 (1999), 1057-1081. (pdf)

19. (with Z. Grujic), Space analyticity for the nonlinear heat equation in a bounded domain, J. Diff. Eq. 154 (1999), 42-54. published version (pdf)

18. Self-similar variables and the complex Ginzburg-Landau equation, Comm. PDE 24 (1999), 545-562. (pdf)

17. (with Z. Grujic), Space analyticity for the Navier-Stokes and related equations with initial data in $L^p$, J. Funct. Anal. 152 (1998), 447-466. (pdf)

16. Quantitative uniqueness for second order elliptic operators, Duke Math. J. 91 (1998), 225-240. (pdf)

15. (with K. Nystrom), Unique continuation on the boundary for Dini domains, Proceedings of AMS 126 (1998), 441-446. published version (pdf)

14. Level sets for the stationary Ginzburg-Landau equation, Calc. Var. 5 (1997), 511-521. published version (pdf)

13. (with P. Constantin, C. Foias, and A. Majda), Dirichlet quotients for periodic 2 dimensional Navier-Stokes equations, J. Math Pures Appl. 76 (1997), 125-153. published version (pdf)

12. (with C. Foias and M. S. Jolly), Localization of attractors by their analytic properties, Nonlinearity 9 (1996), 1565-1581. published version (pdf)

11. Level sets of the vorticity and the stream function for the 2D periodic Navier-Stokes equations with potential forces, J. Diff. Eq. 126 (1995), 374-388. published version

10. Hausdorff measure of level sets for solutions of parabolic equations, Internat. Math. Res. Notices No. 13 (1995) 671-682. (pdf)

9. Nodal volumes for eigenfunctions of analytic regular elliptic problems, J. d'Analyse Mathematique 67 (1995), 269-280. (pdf)

8. (with C. Foias), Determining nodes for the Kuramoto-Sivashinsky equation, J. Dynam. Diff. Eq. 7 (1995), 365-373. published version (pdf)

7. Hausdorff length of level sets for solutions of the Ginzburg-Landau equation, Nonlinearity 8 (1995) , 113-129. published version (pdf)

6. Oscillations of solutions of the Kuramoto-Sivashinsky equation, Physica D 76 (1994), 369-374. published version (pdf)

5. An absence of certain class of periodic solutions in the Navier-Stokes equations, J. Dynam. Diff. Eq. 6 (1994), 175-183. published version (pdf)

4. An upper bound for the winding number for solutions of the Ginzburg-Landau equation, Indiana Univ. Math. J. 41 (1992), 825-836. (pdf)

3. On the number of determining nodes for the Ginzburg-Landau equation, Nonlinearity 5 (1992), 997-1006. published version (pdf)

2. On the behavior of the solutions of the Kuramoto-Sivashinsky equations for negative time, J. Math. Anal. Appl. 166 (1992), 601-606. published version (pdf)

1. On the time analyticity radius of the solutions of the 2 dimensional Navier-Stokes equations, J. Dynam. Diff. Eq. 3 (1991), 611-618. published version (pdf)