My research area is Analysis of Partial Differential Equations. I am currently interested in problems arising in or related to fluid dynamics.

My research is partially supported by NSF grants DMS-1907776, DMS-2205734, DMS- 2205710. My work can be found on my arXiv page and Google Scholar page.

Publications

  1. Transverse instability of Stokes waves at finite depth. arXiv.
  2. Proof of the transverse instability of Stokes waves (with R. Creedon and W. Strauss). Annals of PDE (2024). arXiv.
  3. Slowly traveling gravity waves for Darcy flow: existence and stability of large waves  (with J. Brownfield). Communication in Mathematical Physics (2024). arXiv.
  4. Large traveling capillary-gravity waves for Darcy flow. arXiv.
  5. Global well-posedness for the one-phase Muskat problem in 3D (with H. Dong and F. Gancedo). arXiv.
  6. Traveling wave solutions to the one-phase Muskat problem: existence and stability (with I. Tice). Archive for Rational Mechanics and Analysis (to appear). arXiv.
  7. Modulational instability of classical water waves (with W. Strauss). From Classical Analysis to Analysis on Fractals: A Tribute to Robert Strichartz, Volume 1, page 43-52 (2023).
  8. Coercivity of the Dirichlet-to-Neumann operator and applications to the Muskat problem. Acta Vietnam Mathematica (2023), Special Issue in honor of Prof. Duong Minh Duc. arXiv.
  9. Self-similar solutions for the Muskat problem (with E Garca-Juarez, J Gomez-Serrano, B. Pausader). Advances in Mathematics (2022). arXiv.
  10. Global well-posedness for the one-phase Muskat problem (with H. Dong and F. Gancedo). Communication on Pure and Applied Mathematics (to appear). arXiv.
  11. Remarks on the solution map for Yudovich solutions of the Euler equations. Journal of Mathematical Fluid Mechanics (2022). arXiv.
  12. Bounds on heat flux for Rayleigh-Benard convection between Navier-slip fixed temperature boundaries (with T. D. Drivas and C. Nobili). Philosophical Transactions of the Royal Society A, Special Issue: Mathematical Problems in Physical Fluid Dynamics" (2022). arXiv. 
  13. Well-posedness for SQG sharp fronts with unbounded curvature (with F. Gancedo and N. Patel). Mathematical Models and Methods in Applied Sciences (2022). arXiv.
  14. Global solutions for the Muskat problem in the scaling invariant Besov space. Advances in Mathematics (2022). arXiv.
  15. Proof of modulational instability of Stokes waves in deep water (with W. A. Strauss). Communication on Pure and Applied Mathematics (2022). arXiv.
  16. The vanishing surface tension limit of the Muskat problem (with P. Flynn). Communication in Mathematical Physics (2021). arXiv.
  17. On well-posedness of the Muskat problem with surface tension. Advances in Mathematics (2020). arXiv.
  18. A paradifferential approach for well-posedness of the Muskat problem (with B. Pausader). Archive for Rational Mechanics and Analysis (2020). arXiv.
  19. On global stability of optimal rearrangement maps (with Toan T. Nguyen). Archive for Rational Mechanics and Analysis (2020). arXiv.
  20. Compressible fluids and active potentials (with P. Constantin, T. D. Drivas, F. Pasqualotto). Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (2020). arXiv
  21. Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit (with T. D. Drivas). Journal of Nonlinear Science (2019). arXiv.
  22. Inviscid limit for SQG in bounded domains (with P. Constantin, M. Ignatova). SIAM Journal of Mathematical Analysis (2018). arXiv.
  23. Onsager's conjecture and anomalous dissipation on domains with boundary (with T. D. Drivas). SIAM Journal of Mathematical Analysis (2018). arXiv.
  24. On singularity formation in a Hele-Shaw model (with P. Constantin, T. Elgindi, V. Vicol). Communication in Mathematical Physics (2018). arXiv.
  25. Local and global strong solutions for SQG in bounded domains (with P. Constantin). Physica D, Special Issue: Nonlinear PDE in Mathematical Fluid Dynamics (2018). arXiv.
  26. Global weak solutions for generalized SQG in bounded domains. Analysis & PDE (2018). arXiv.
  27. Global weak solutions for SQG in bounded domains (with P. Constantin) . Communication on Pure and Applied Mathematics (2018). arXiv.
  28. Sharp Strichartz estimates for water waves systems. Transactions of the American Mathematical Society (2018). arXiv.
  29. A sharp Cauchy theory for 2D gravity-capillary water waves. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (2017). arXiv.
  30. Strichartz estimates and local existence for the gravity-capillary water waves with non-Lipschitzinitial velocity (with T. de Poyferre). Journal of Differential Equations (2016). arXiv.
  31. A paradifferential reduction for the gravity-capillary waves system at low regularity and applications (with T. de Poyferre). Bulletin de la Societe Mathematique de France (2017). arXiv.
  32. A pseudo-local property of gravity water waves system. SIAM Journal of Mathematical Analysis (2016). arXiv.
  33. Hadamard well-posedness of the gravity water waves system. Journal of Hyperbolic Differential Equations (2016). arXiv.

Collaborators

P. Constantin (Princeton), T. de Poyferre, R. Creedon (U. Washington), H. Dong (Brown), T. D. Drivas (Stony Brook), T. Elgindi (Duke), P. Flynn (Brown), F. Gancedo (Sevilla, Spain), E Garca-Juarez (Brown), J Gomez-Serrano (Brown), M. Ignatova (Temple), Toan Nguyen (Penn State),  C. Nobili (Hamburg, Germany) N. Patel (ICMAT, Spain),  F. Pasqualotto (Berkeley), B. Pausader (Brown), W. Strauss (Brown), I. Tice (CMU), V. Vicol (Courant).