Igor Kukavica Professor of Mathematics Contact Information E-mail: kukavica@math.usc.edu Phone: (213) 740-3781 Office: KAP 262C LINKS Faculty Profile on Departmental Website

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

Conferences and Other Presentations

Conference Presentations

• "Regularity of the primitive equations of the ocean", AMS sectional meeting, Chicago, Fall 2007, Talk/Oral Presentation, , Chicago, IL, AMS, Invited, 10/06/2007-  
• "Regularity and uniform gradient bounds for solutions of the primitive equations of the ocean", AIMS meeting, Talk/Oral Presentation, , Arlington, TX, AIMS, Invited, 05/21/2008  
• "On partial regularity for the Navier-Stokes equations", AMS sectional meeting, Spring 2008, Talk/Oral Presentation, , Bloomington, IN, AMS, Invited, 04/05/2008  
• "On partial regularity for the Navier-Stokes equations", SIAM conference on Analysis of Partial Differential Equations, Lecture/Seminar, , Phoenix, AZ, SIAM, Invited, 12/10/2007  
• "Decay properties of solutions of the Navier-Stokes equations", Keynote Lecture, , Tempe, AZ, Arizona State University, Invited, 11/19/2007  
• "Conditional regularity and thin domain results for solutions of the navier-Stokes equaations", workshop Partial differential equations and fluid mechanics, Talk/Oral Presentation, , University of Warwick, UK, University of Warwick, Invited, 05/21/2007  
• "Decay properties of solutions of the Navier-Stokes equations ", AMS sectional meeting, Miami University, Talk/Oral Presentation, , Miami University, Oxford, OH, AMS, Invited, 03/17/2007  
• " Existence of solutions of the Navier-Stokes equations in a thin periodic domain with large data", AMS sectional meeting, Univ. of Arkansas, Fayetteville, Talk/Oral Presentation, , Univ. of Arkansas, Fayetteville, ams, Invited, 11/03/2006  

Other Presentations

• "Conditional regularity and thin domain results for solutions of the Navier-Stokes equations", Applied Mathematics Colloquium, Penn State University, State College, PA, 04/11/2008  
• "Partial regularity for the Navier-Stokes equations", Colloquium, University of Virginia, Charlottesville, VA, 04/10/2008  
• "An introduction for the regularity and partial regularity of the Navier-Stokes equations", Graduate colloquium, USC, USC, Los Angeles, CA, 03/24/2008  
• "Dirichlet quotients and backward uniqueness for parabolic PDEs", Analysis seminar, USC, USC, Los Angeles, CA, 02/15/2008  
• "Conditional regularity and thin domain results for solutions of the Navier-Stokes", PDE seminar, University of Virginia, Charlottesville, Virginia, 03/14/2007  
• " Conditional regularity for solutions of the Navier-Stokes equations", PDE seminar, UC San Diego, San Diego, CA, 01/11/2007  
• " Conditional regularity for solutions of the Navier-Stokes equations ", PDE seminar, Indiana Univ., Bloomington, IN, 10/11/2006  
• "Size of nodal sets for solutions of hither order parabolic PDEs", PDE seminar, University of Notre Dame, 10/10/2006  

Publications

Journal Article

• 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. (2008). Uniform gradient bounds for the primitive equations of the ocean. Differential Integral Equations. Vol. 21 (9-10), pp. 837-849.
• Kukavica, I. (2008). Regularity for the Navier-Stokes equations with a solution in a Morrey space. Indiana University Mathematics Journal.
• 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. (2008). On the weighted decay for solutions of the Navier-Stokes system. Nonlinear Analysis.
• 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., 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. (2005). Log-log convexity and backward uniqueness. Proceedings, Amer. Math. Soc./American Mathematical Society. Vol. to a, pp. pear.
• 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.

Service to the University

Administrative Appointments

• Graduate Vice-Chair, 08/2005-  

Committees

• Member, CAMS Colloquium co-organizer, 08/20/2008-  
• coorginizer of the Analysis Graduate Student Seminar, 2005-  
• coorginizer of the Analysis seminar, 2005-  
• 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-