Jiten Kumbhakar Postdoctoral Researcher in Mathematics
PDEs · Fluid Mechanics · Control Theory

Analysis and control of nonlinear PDEs arising in fluid mechanics.

I am a postdoctoral researcher at the Institute of Mathematics, Czech Academy of Sciences. My research focuses on partial differential equations arising in fluid mechanics and control theory.

My current interests include compressible Navier–Stokes equations, time-periodic problems, controllability and stabilization, fluid–structure interaction, and critical-space methods based on harmonic analysis.

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Current research

Research directions

Full research overview →
01

Time-Periodic Fluid Equations

Existence, regularity, stability, and control of time-periodic solutions for compressible fluid systems and related non-autonomous evolution problems.

Compressible Navier–StokesEvolution familiesPeriodic solutions
02

Fluid–Structure Interaction

Weak solutions and analytical questions for compressible fluid–rigid body systems, including moving domains, thermodynamic effects, and energy methods.

Joint work with Kuntal Bhandari and Šárka Nečasová.

FSIWeak solutionsEnergy & entropy
03

Control of PDEs and Fluid Flows

Boundary and distributed controllability, stabilization, spectral methods, observability, and turnpike-type questions for evolution equations.

ControllabilityStabilizationObservability
04

Critical-Space Analysis

Well-posedness and long-time estimates using Littlewood–Paley theory, Besov spaces, Fourier analysis, transport estimates, and nonlinear product bounds.

Besov spacesLittlewood–PaleyTransport estimates
Updates

Recent & upcoming

  • Oct 2026
    Seminar talks in Prague.

    Presentations on time-dependent Besov-space methods and time-periodic compressible fluid problems.

  • Sep 2026
    Current projects.

    Ongoing work on time-periodic compressible Navier–Stokes equations and compressible fluid–structure interaction.

  • 2026
    New publication in JDE.

    “Boundary null-controllability of 1D linearized compressible Navier–Stokes system by one control force.”

Research Notes

Working notes on tools for PDEs and control

Short expository notes collecting analytical ideas that repeatedly appear in my research and teaching.

  • Besov Spaces & Littlewood–Paley TheoryPlanned
  • Carleman Estimates & ObservabilityPlanned
  • Semigroups & Evolution FamiliesPlanned
  • Moment Methods in PDE ControlPlanned
Open research notes
Selected work

Publications & manuscripts

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  • Boundary null-controllability of 1D linearized compressible Navier–Stokes system by one control force
    K. Bhandari, S. Chowdhury, R. Dutta, and J. Kumbhakar
    Journal of Differential Equations, 453 (2026), Article 113891. DOI
  • Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a Neumann control
    K. Bhandari, J. Kumbhakar, and S. Majumdar
    Evolution Equations and Control Theory, 13(2), 587–615, 2024. DOI
  • Null controllability of one-dimensional barotropic and non-barotropic linearized compressible Navier–Stokes system using one boundary control
    J. Kumbhakar
    Submitted arXiv
About

Academic background

I received my Ph.D. in Mathematics from IISER Kolkata, where I worked under the supervision of Dr. Shirshendu Chowdhury on boundary controllability problems for compressible Navier–Stokes systems and related equations.

Since 2025, I have been a postdoctoral researcher in Prague, broadening my work toward time-periodic fluid equations, fluid–structure interaction, and nonlinear PDE analysis.