Igor Kukavica

• Assistant Professor, University of Chicago, 10/1995 – 09/1997
• Dickson Instructor, University of Chicago, 10/1993 – 09/1995

Tenure Track Appointments

• Professor, University of Southern California, 09/2004 –
• Associate Professor, University of Southern California, 09/1998 – 08/2004
• Assistant Professor, University of Southern California, 08/1997 – 08/1998

Research, Teaching, Practice, and Clinical Appointments

• Assistant Professor, University of Chicago, 1995-09-1997-08

PostDoctoral Appointments

• Dickson Instructor, University of Chicago, 09/1993 – 08/1995

Summary Statement of Research Interests

Professor Kukavica’s research interests include exploration of partial differential equations, nonlinear dynamics, and Navier-Stokes Equations.

Journal Article

• Kukavica, I. (2011). Partial regularity for the Navier-Stokes eqautions with a force in a Morrey space. J. Math. Anal. Appl.. Vol. 374, pp. 573-584.
• Kukavica, I., Vicol, V. (2011). Domain of analyticity for solutions of the three-dimensional Euler equations in half space. Discrete Cont. Dynamical Systems. Vol. 29, pp. 285-303.
• Kukavica, I., Tuffaha, A., Ziane, M. (2011). Strong solutions to a Navier-Stokes-Lame system on a domain with a non-flat boundary. Nonlinearity. Vol. 24, pp. 159-176.
• Kukavica, I., Reis, E. (2011). Asymptotic expansion for solutions of the Navier-Stokes equations with potential forces. Journal of Differential Equations. Vol. 250, pp. 607-625.
• Kukavica, I., Temam, R., Vicol, V., Ziane, M. (2011). Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. Journal of Differential Equations. Vol. 250, pp. 1719-1746.
• Kukavica, I., Vicol, V. (2011). On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations. Nonlinearity. Vol. 24, pp. 765-796.
• Kukavica, I., Tuffaha, A. (2011). Solutions to a fluid-structure interaction free boundary problem. Discrete and Continuous Dynamical Systems.
• Ignatova, M., Kukavica, I. (2011). Strong unique continuation for higher order elliptic equations with Gevrey coefficients. Journal of Differential Equations.
• Kukavica, I., Tuffaha, A., Ziane, M. (2010). Strong solutions to a fluid structure interaction system. Advances in Differential Equations. Vol. 15 (3-4), pp. 231-254.
• Kukavica, I. (2010). On regularity for the Navier-Stokes equations in Morrey space. Discrete and Continuous Dynamical Systems. Vol. 26, pp. 1319-1328.
• Kukavica, I., Ignatova, M. (2010). Unique continuation and complexity of solutions to parabolic partial differential equations with Gevrey coefficients. Advances in Differential Equations. Vol. 15, pp. 953-975.
• Kukavica, I., Temam, R., Vicol, V., Ziane, M. (2010). Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. C. R. Math. Acad. Sci. Paris. Vol. 384, pp. 639-645.
• Kukavica, I. (2009). On the weighted decay for solutions of the Navier-Stokes system. Nonlinear Analysis.
• Kukavica, I. (2009). On the Radius of Analyticity of Solutions to the Three-Dimensional Euler Equations. Proceeedings of AMS. Vol. 137 (2), pp. 669-677.
• Kukavica, I., Ziane, M., Tuffaha, A. (2009). Strong solutions to a nonlinear fluid structure interaction system. Journal of Differential Equations. Vol. 247, pp. 1452-1478.
• Kukavica, I. (2009). The fractal dimension of the singular set for solutions of the Navier-Stokes system. Nonlinearity. Vol. 22, pp. 2889-2900.
• Kukavica, I. (2008). Regularity for the Navier-Stokes equations with a solution in a Morrey space. Indiana University Mathematics Journal. Vol. 57, pp. 2843-2860.
• Kukavica, I., Ziane, M. (2008). Uniform gradient bounds for the primitive equations of the ocean. Differential Integral Equations. Vol. 21 (9-10), pp. 837-849.
• Kukavica, I. (2008). On partial regularity for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems.
• Kukavica, I., Vicol, V. (2008). On local uniqueness of weak solutions to the Navier-Stokes system with BMO-1 initial datum. J. Dyn. Diff. Equat.. Vol. 20, pp. 719-732.
• Kukavica, I., Ziane, M. (2008). On the regularity of the primitive equations of the ocean. Nonlinearity. Vol. 20
• Kukavica, I., Ziane, M. (2008). The regularity of solutions of the primitive equations of the ocean in space dimension three. C.R. Math. Acad. Sci. Paris. Vol. 345, pp. 257–260.
• Kukavica, I., Torres, J. J. (2007). Weighted $L^p$ decay for solutions of the Navier-Stokes equations. Communications in Partial Differential Equations/Taylor & Francis. Vol. to a, pp. pear.
• Kukavica, I., Ziane, M. (2007). Sur la regularite des solutions des equations de Navier-Stokes dans un domaine mince periodique de faible epaisseur. C. R. Math. Acad. Sci. Paris. Vol. 344, pp. 97-102.
• Kukavica, I. (2007). On the regularity of the Navier-Stokes equation in a thin periodic domain. J. Diff. Eq.. Vol. 234, pp. 485-506.
• Kukavica, I. (2007). Log-log convexity and backward uniqueness. Proceedings, Amer. Math. Soc./American Mathematical Society. Vol. 135, pp. 2415-2421.
• Kukavica, I., Ziane, M. B. (2006). Regularity of the Navier-Stokes equation in a thin periodic domain with large data. Discrete and Continuous Dynamical Systems (B)/American Institute of Mathematical Sciences. Vol. Vol 16 (No 1), pp. (2006) pp. 67-86.
• Kukavica, I., Ziane, M. B. (2006). Navier-Stokes equation with regularity in one direction. Journal of Mathematical Physics/American Institute of Physics. Vol. NA
• Kukavica, I. (2006). Role of the pressure for validity of the energy equality for solutions of the Navier-Stokes equation. Journal of Dynamics and Differential Equations/Elsevier. Vol. 343-31-36
• Kukavica, I. (2006). Pressure integrability conditions for uniqueness of mild solutions. Journal of Differential Equations/Elsevier. Vol. 223, pp. 427-441.
• Kukavica, I., Ziane, M. B. (2006). One component regularity for the Navier-Stokes equation. Nonlinearity/Institute of Physics. Vol. Vol 19 (No 2), pp. (2006) pp.453-469.
• Kukavica, I., Ziane, M. B. (2006). Regularite conditonnelle des equations de Navier-Stokes. Comptes Rendus de l’Academie des Sciences de Paris, Mathematiques/Elsevier. Vol. Vol 343 (No 1), pp. (2206) pp. 31-36.
• Kukavica, I., Torres, J. J. (2005). Weighted bounds for the velocity and the vorticity for the Navier-Stokes equations,. Nonlinearity/Institute of Physics. Vol. 19 (2006), pp. 293-303.
• Kukavica, I. (2005). On Fourier Parametrization of Global Attractors for Equations in One Space Dimension. Discrete and Continuous Dynamical Systems (B)/American Institute of Mathematical Sciences. Vol. 13, pp. 553-560.
• Kukavica, I., Malcok, M. (2005). Backward behavior of solutions of the Kuramoto-Sivashinsky equation,. Journal of Mathematical Analysis and Applications/Elsevier. Vol. 307 455-464

Proceedings

• Kukavica, I. (2009). Partial regularity results for solutions of the Navier-Stokes system. Springer.

Other

• Kukavica, I. (2003). A remark on time-analyticity for the Kuramoto-Sivashinsky equation.
• Kukavica, I. (2001). Space-time decay for solutions of the Navier-Stokes equations, Indiana Univeristy Math. J. 50, 2001, Special Issue, 205-222.
• Kukavica, I. (2000). Interior gradient bounds for the 2D Navier-Stokes system, Discrete Contin. Dynam. Systems 7, 2001, no. 4, 873–882.
• Kukavica, I. (2000). Nodal parametrisation of analytic attractors. Discrete Contin. Dynam. Systems 7, 2001, no. 3, 643–657.

Administrative Appointments

• Graduate Vice-Chair, 08/2005 – 12/2011

Committees

• coorginizer of the Analysis Graduate Student Seminar, 2005 –
• coorginizer of the Analysis seminar, 2005 –
• Member, CAMS Colloquium co-organizer, 08/20/2008 – 12/20/2011
• Member, Graduate Advisory Committee, 2007-2008

Conferences Organized

• Member of the Organizing Committee, Mathematics of Fluids, USC, 2007-2008

Editorships and Editorial Boards

• Editorial Board member, Communications on Pure and Applied Analysis, 09/01/2005 –