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Igor Kukavica

Professor of Mathematics

Contact Information
E-mail: kukavica@usc.edu
Phone: (213) 740-3781
Office: KAP 262C

LINKS
Faculty Profile on Departmental Website
Personal Website
 

Education

Ph.D. Mathematics, Indiana University, 8/1993
 

Postdoctoral Training

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

Academic Appointment, Affiliation, and Employment History

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  
 

Non-Tenure Track Appointments

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

PostDoctoral Appointments

Dickson Instructor, University of Chicago, 09/1993-08/1995  
 

Description of Research

Summary Statement of Research Interests

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

Publications

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
 

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.
 

Proceedings

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

Service to the University

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   
 

Service to the Profession

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-  
 
 
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