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:


  • 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


  • 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)

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