Publications
40. Z. Brzeźniak, A. Larios, I. Safarik. Fractional Voigt-regularization of the 3D Navier-Stokes and Euler equations: Global well-posedness and limiting behavior arXiv:2410.23492
39. M. Enlow, A. Larios, and Y. Pei. Calmed Ohmic Heating for the 2D Magnetohydrodynamic-Boussinesq System: Global Well-posedness and Convergence. (submitted) arXiv:2410.04357.
38. P. Howard, A. Larios, and Q. Lin. Comparison of coarsening dynamics for the Cahn–Hilliard and Burgers–Cahn–Hilliard equations. (submitted) arXiv:2405.11709.
37. A. Larios and I. Safarik. A note on explicit convergence rates of nonlocal peridynamic operators in Lq-norm. (submitted) arXiv:2402.16303.
36. A. Larios and V. R. Martinez. Remarks on the stabilization of large-scale growth in the 2D Kuramoto–Sivashinsky equation. J. Math. Fluid Mech., 26(4):1–21, 2024. doi:10.1007/s00021-024-00890-3, [url], [arXiv].
35. M. Enlow, A. Larios, and J. Wu. Calmed 3D Navier–Stokes equations: Global well-posedness, energy identities, and convergence. J. Nonlinear Sci. 34, 112, 2024. doi.org/10.1007/s00332-024-10093-9, [url], [arXiv].
34. A. Larios, M. R. Petersen, and C. Victor. Application of continuous data assimilation in high-resolution ocean modeling. Commun. Comput. Phys., 35(5):1418–1444, 2024. doi:10.4208/cicp.OA-2023-0208, [url], [arXiv].
33. A. Larios and C. Victor. Continuous data assimilation for the 3D and higher-dimensional Navier–Stokes equations with higher-order fractional diffusion. J. Math. Anal. Appl.:128644, 2024. doi:10.1016/j.jmaa.2024.128644, [url], [arXiv].
32. F. Scabbia, C. Gasparrini, M. Zaccariotto, U. Galvanetto, A. Larios, and F. Bobaru. Moving interfaces in peridynamic diffusion models and influence of discontinuous initial conditions: Numerical stability and convergence. Comput. Math. Appl., 151:384–396, 2023. doi:10.1016/j.camwa.2023.10.016, [url], [SSRN].
31. M. Enlow, A. Larios, and J. Wu. Algebraic calming for the 2D Kuramoto–Sivashinsky equations. Nonlinearity, 37, 11, 2024. doi:10.1088/1361-6544/ad792e, [url], [arXiv].
30. E. Carlson, A. Larios, and E. S. Titi. Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: the 2D Navier–Stokes equations paradigm. J. Nonlin. Sci., 34(2):37, 2024. doi:10.1007/s00332-024-10014-w, [url], [arXiv].
29. A. Larios, Y. Pei, C. Victor, The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier-Stokes equations. (submitted) [arXiv]
28. A. Farhat, A. Larios, V. R. Martinez, and J. P. Whitehead. Identifying the body force from partial observations of a two-dimensional incompressible velocity field. Phys. Rev. Fluids, 9:054602, 5, 2024. doi:10.1103/PhysRevFluids.9.054602, [url], [arXiv].
27. A. Larios and Y. Pei. Nonlinear continuous data assimilation. Evol. Equ. Control Theory, 13(2):329–348, 2024. doi:10.3934/eect.2023048, [url], [arXiv].
26. J. Zhao, A. Larios, and F. Bobaru. Construction of a peridynamic model for viscous flow. J. Comput. Phys., 468:111509, 2022. doi:10.1016/j.jcp.2022.111509, [url], [SSRN].
25. T. Franz, A. Larios, and C. Victor. The bleeps, the sweeps, and the creeps: Convergence rates for dynamic observer patterns via data assimilation for the 2D Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg., 392:Paper No. 114673, 19, 2022. doi:10.1016/j.cma.2022.114673, [url], [arXiv].
24. E. Carlson, J. Hudson, A. Larios, V. R. Martinez, E. Ng, and J. Whitehead. Dynamically learning the parameters of a chaotic system using partial observations. Discrete Contin Dyn Syst Ser A, 42(8):3809–3839, 2022. doi:10.3934/dcds.2022033, [url], [arXiv].
23. S. Jafarzadeh, F. Mousavi, A. Larios, and F. Bobaru. A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture. Comput. Methods Appl. Mech. Engrg., 392:114666, 2022. doi:10.1016/j.cma.2022.114666, [url], [arXiv].
22. E. Carlson, L. Van Roekel, H. Godinez, M. Petersen, A. Larios, Exploring a New Computationally Efficient Data Assimilation Algorithm For Ocean Models. (submitted) doi:10.1002/essoar.10507378.1, [url],
21. A. Larios, M. M. Rahman, K. Yamazaki, Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three. J. Nonlinear Sci. 32(6) (2022), 1–33. doi:10.1007/s00332-022-09828-3, [url], [arXiv].
20. E. Carlson, A. Larios. Sensitivity analysis for the 2D Navier-Stokes equations with applications to continuous data assimilation. J. Nonlin. Sci., 31, 5, (2021). doi:10.1007/s00332-021-09739-9, [url], [arXiv].
19. S. Jafarzadeh, L. Wang. A. Larios, F. Bobaru, A fast convolution-based method for peridynamic transient diffusion in arbitrary domains. Comput. Methods Appl. Mech. Engrg., 375, Paper No. 113633, (2021). doi:10.1016/j.cma.2020.113633, [url], [arXiv].
18. M. Gardner, A. Larios, L.G. Rebholz, D. Vargun, C. Zerfas, Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. AIMS Electronic Research Archive. 29, no. 1 (2021), 2223-2247. doi:10.3934/era.2020113, [url],
17. A. Larios, C. Victor, Continuous data assimilation with a moving cluster of data points for a reaction diffusion equation: A computational study. Commun. Comp. Phys. 29 (2021), 1273-1298. doi:10.4208/cicp.oa-2018-0315, [url], [arXiv].
16. A. Larios, K. Yamazaki, On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation. Physica D. 411 (2020), 1-14. doi:10.1016/j.physd.2020.132560, [url], [arXiv].
15. S. Jafarzadeh, A. Larios, F. Bobaru, Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods J. Peridynam. Nonlocal Modeling. 2, no. 1 (2020), 85-110. doi:10.1007/s42102-019-00026-6, [url], [arXiv].
14. E. Carlson, J. Hudson, A. Larios, Parameter recovery and sensitivity analysis for the 2D Navier-Stokes equations via continuous data assimilation. SIAM J. Sci. Comput. 42, no. 1 (2020), 250-270. doi:10.1137/19M1248583, [url], [arXiv].
13. A. Larios, Y. Pei, Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data. Evol. Equ. Control Theory. 9 (2020), no. 3, 733–751. doi:10.3934/eect.2020031, [url], [arXiv].
12. A. Larios, L. G. Rebholz, C. Zerfas, Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 345 (2019), 1077–1093. doi:10.1016/j.cma.2018.09.004, [url], [arXiv].
11. A. Larios, Y. Pei, L. G. Rebholz, Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations. J. Differential Equations 266 (2019), no. 5, 2435–2465. doi:10.1016/j.jde.2018.08.033, [url], [arXiv].
10. A. Biswas, J. Hudson, A. Larios, and Y. Pei, Continuous data assimilation for the magnetohydrodynamic equations in 2D using one component of the velocity and magnetic fields. Asymptotic Anal. 108 (2018), no. 1-2, 1-43. doi:10.3233/ASY-171454, [url], [pdf].
9. A. Larios, B. Wingate, M. Petersen, E. S. Titi, The Euler-Voigt equations and a computational investigation of the finite-time blow-up of solutions to the 3D Euler Equations Theor. Comp. Fluid Dyn. 3, no.~1 (2018), 23-34. doi:10.1007/s00162-017-0434-0, [url], [arXiv].
8. A. Larios, Y. Pei, On the local well-posedness and a Prodi-Serrin type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion. J. Differential Equations. 263 (2017), no. 2, 1419-1450. 10.1016/doi:j.jde.2017.03.024, [url], [arXiv].
7. A. Biswas, C. Foias, and A. Larios, On the attractor for the semi-dissipative Boussinesq equations. Ann. Inst. H. Poincaré Anal. Non Linéaire. 34 (2017), no. 2, 381-405. doi:10.1016/j.anihpc.2015.12.006, [url], [arXiv].
6. A. Larios, E.S. Titi, Some paradigms on the effect Of boundary conditions on the global regularity and singularity of non-linear partial differential equations. Recent progress in the theory of the Euler and Navier-Stokes equations, 96–125, London Math. Soc. Lecture Note Ser., 430, Cambridge Univ. Press, Cambridge, 2016. doi:10.1007/cbo9781316407103.007, [url], [arXiv].
5. J.-L. Guermond, A. Larios, T. Thompson, Validation of an entropy-viscosity model for large eddy simulation. Direct and Large-Eddy Simulation IX, ERCOFTAC Series, 20 (2015), 43-48. doi:10.1007/978-3-319-14448-1_6, [url], [pdf].
4. A. Larios and E.S. Titi, Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations. J. Math. Fluid Mech. 16 (2014), no. 1, 59-76. doi:10.1007/s00021-013-0136-3, [url], [pdf].
3. A. Larios, E. Lunasin, and E.S. Titi, Global well-posedness for the 2D Boussinesq system without heat diffusion and with either anisotropic viscosity or inviscid Voigt-α regularization. J. Differential Equations. 255 (2013) 2636-2654. doi:10.1016/j.jde.2013.07.011, [url], [pdf].
2. P. Kuberry, A. Larios, L.G. Rebholz, N.E. Wilson, Numerical approximation of the Voigt regularization of incompressible Navier-Stokes and magnetohydrodynamic flows, Computers & Mathematics with Applications 64(8) (2012), 2647-2662. doi:10.1016/j.camwa.2012.07.010, [url], [pdf].
1. A. Larios and E.S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models, Discrete and Continuous Dynamical Systems B, 14(2) (2010), 603-627. (An invited article for a special issue in honor of Professor P. Kloeden on the occasion of his 60th birthday) doi:10.3934/dcdsb.2010.14.603, [url], [pdf].