Home Page of Sundar


Name: Padmanabhan Sundar

Position: Professor

Degree Credentials: Ph. D., Purdue University.

Office Location and Phone:316, Lockett; 225-578-1611

E-mail Address: sundar at math.lsu.edu

Courses Taught: Spring 2017:
Math 3355 (10:20 - 11:50 T Th in Lockett 112)

Office Hours: M, W, Th.: 2:00 - 3:00

Research interests: I am interested in probabilistic aspects of fluid dynamics and turbulence. I currently work on the Navier-Stokes equations in two-dimensions on a bounded domain for incompressible viscous fluid flow. Stationary measures, ergodic behavior, optimal time-average control, perturbation by fractional Brownian noise, backward stochastic Navier-Stokes equations, and large deviation results for solutions of stochastic Navier-Stokes equations form a list of research problems that I have studied. My research interests are based on the semimartingale theory, stochastic differential equations, martingale problems, interacting particle systems, and the large deviations principle.

Recent Publications:

Books:

  • Stochastic Analysis and Diffusion Processes written by Gopinath Kallianpur and P. Sundar, Oxford Graduate Texts in Mathematics 24, January 2014.

  • The book is available at Oxford University Press: http://ukcatalogue.oup.com/product/9780199657070.do

    Papers:

  • The Enskog Process; Journal of Statistical Physics, accepted 2016 (joint work with S. Albeverio, B. Ruediger) pdf

  • The law of the iterated logarithm for a class of SPDEs; submitted 2016 (joint work with P. Fatheddin)

  • Existence of solutions for a class of semilinear evolution equations with impulses and delays; submitted 2016 (joint work with H. Leiva) pdf

  • Two-dimensional stochastic Navier-Stokes equations with fractional Brownian noise; Random Operators and Stochastic Equations , 21, 135 - 158, 2013. (joint work with L. Fang and F. Viens)| pdf

  • Towards a Resolution of the Reference Pressure Controversy in Cerebrospinal Fluid Flow Dynamics; Cerebrospinal Fluid: Functions, Composition and Disorders, Ed. V. Slavik and T. Dolezal, Nova Science Publishers, 107-121, 2012. (Joint work with Kalyan Raman)

  • A Representation for Positive Functionals of a Brownian Motion and an Application, Communications on Stochastic Analysis , 6, 669-687, 2012. (joint work with Ming Tao)

  • Stochastic MHD System perturbed by a general noise; Communications on Stochastic Analysis , {\bf 4}, 253-269, 2010.

  • Large deviations for the stochastic shell model of turbulence ; Nonlinear Differential Equations and Applications ,16, 493-521, 2009. (joint work with U. Manna and S.S. Sritharan)

  • Existence and Uniqueness of Solutions to the Backward 2D Stochastic Navier-Stokes Equations; Stochastic Processes and their Appl., 119, 1216-1234, 2009. (joint work with Hong Yin)|pdf

  • Adapted Solutions to the Backward Stochastic Navier-Stokes Equations in 3D; Infinite Dimensional Stochastic Analysis: In Honor of H.-H. Kuo ,World Scientific, 114-134, 2008. (joint work with Hong Yin)

  • Existence and Uniqueness of Solutions to the Backward Stochastic Lorenz System ; Comm. on Stoch. Analysis , 1, no. 3, 473-483, 2007. (joint work with Hong Yin)

  • Large Deviations for the Two-Dimensional Navier-Stokes Equations with Multiplicative Noise ; Stochastic Processes and their Appl., 116, 1636-1659, 2006. (joint work with S.S. Sritharan) | pdf

  • A note on the solution of a stochastic partial differential equation; Stochastic Analysis and Appl., 22, 923-938, 2004.

  • Two applications of reproducing kernel Hilbert spaces in stochastic analysis; Stochastics in Finite and Infinite Dimensions: In Honor of G. Kallianpur, ed. T. Hida et al., Trends in Mathematics Series, Birkhauser, 195-206, 2001. (joint work with T. Koski)

  • Comparison of solutions of stochastic equations and applications; Stochastic Anal. Appl., 18, 211-229, 2000. (joint work with G. Ferreyra)

  • Ergodic Control of Stochastic Navier-Stokes Equation; Nonlinear problems in Aviation and Aerospace, ed. S. Sivasundaram, Gordon Breach Publications, 213-221, 2000. (joint work with S.S. Sritharan)

  • Hilbert Space Valued Super Brownian Motion and Related Evolution Equations; J. of Appl. Math. and Optim., 41, 111-128, 2000. (joint work with G. Kallianpur)

  • Comparison of stochastic Volterra equations; Bernoulli, 6, 1001-1006, 2000.(joint work with G. Ferreyra)

  • Weak convergence of systems of interacting SDEs to the superprocess; J. of Appl. Math. and Optim., 41, 141-154, 2000. (joint work with A. Bose)

  • MSRI Information:
    MSRI Programs (jpg)

    The following are examples of links to other interesting pages:


    The statements and opinions expressed in this page are those of Login Name TTY Idle When Where and may not reflect the views of the Department or the University.


    To request a link from the departmental page to this page, or express comments or suggestions, send E-mail to webmaster@math.lsu.edu.