Citation: Roberta Bianchini, Chiara Saffirio. Fluid instabilities, waves and non-equilibrium dynamics of interacting particles: a short overview[J]. Mathematics in Engineering, 2023, 5(2): 1-5. doi: 10.3934/mine.2023033
[1] | G. B. Apolinário, L. Chevillard, Space-time statistics of a linear dynamical energy cascade model, Mathematics in Engineering, 5 (2023), 1–23. http://doi.org/10.3934/mine.2023025 doi: 10.3934/mine.2023025 |
[2] | G. Basile, D. Benedetto, E. Caglioti, L. Bertini, Large deviations for a binary collision model: energy evaporation, Mathematics in Engineering, 5 (2023), 1–12. http://doi.org/10.3934/mine.2023001 doi: 10.3934/mine.2023001 |
[3] | J. Bedrossian, N. Masmoudi, Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations, Publ. math. IHES, 122 (2015), 195–300. http://doi.org/10.1007/s10240-015-0070-4 doi: 10.1007/s10240-015-0070-4 |
[4] | G. Bevilacqua, Symmetry break in the eight bubble compaction, Mathematics in Engineering, 4 (2022), 1–24. http://doi.org/10.3934/mine.2022010 doi: 10.3934/mine.2022010 |
[5] | T. Buckmaster, C. De Lellis, L. Székelyhidi Jr., Dissipative Euler flows with Onsager-critical spatial regularity, Commun. Pure Appl. Math., 69 (2016), 1613–1670. http://doi.org/10.1002/cpa.21586 doi: 10.1002/cpa.21586 |
[6] | C. Collot, P. Germain, Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting, 2021, arXiv: 2107.11819. |
[7] | G. Crippa, C. Schulze, Sub-exponential mixing of generalized cellular flows with bounded palenstrophy, Mathematics in Engineering, 5 (2023), 1–12. http://doi.org/10.3934/mine.2023006 doi: 10.3934/mine.2023006 |
[8] | Y. C. de Verdière, L. Saint-Raymond, Attractors for two-dimensional waves with homogeneous Hamiltonians of degree 0, Commun. Pure Appl. Math., 73 (2020), 421–462. http://doi.org/10.1002/cpa.21845 doi: 10.1002/cpa.21845 |
[9] | D. Del Santo, F. Fanelli, G. Sbaiz, A. Wróblewska-Kamińska, On the influence of gravity in the dynamics of geophysical flows, Mathematics in Engineering, 5 (2023), 1–33. http://doi.org/10.3934/mine.2023008 doi: 10.3934/mine.2023008 |
[10] | C. De Lellis, L. Székelyhidi Jr., Dissipative Euler flows and Onsager's conjecture, J. Eur. Math. Soc., 16 (2014), 1467–1505. http://doi.org/10.4171/JEMS/466 doi: 10.4171/JEMS/466 |
[11] | Y. Deng, Z. Hani, Full derivation of the wave kinetic equation, 2021, arXiv: 2104.11204. |
[12] | M. Duerinckx, On nonlinear Schrödinger equations with random initial data, Mathematics in Engineering, 4 (2022), 1–14. http://doi.org/10.3934/mine.2022030 doi: 10.3934/mine.2022030 |
[13] | G. E. Fal'kovich, A. V. Shafarenko, Nonstationary wave turbulence, J. Nonlinear Sci., 1 (1991), 457–480. |
[14] | S. Federico, G. Staffilani, Sharp Strichartz estimates for some variable coefficient Schrödinger operators on $\mathbb{R}\times \mathbb{T}^2$, Mathematics in Engineering, 4 (2022), 1–23. http://doi.org/10.3934/mine.2022033 doi: 10.3934/mine.2022033 |
[15] | R. Feola, F. Iandoli, F. Murgante, Long-time stability of the quantum hydrodynamic system on irrational tori, Mathematics in Engineering, 4 (2022), 1–24. http://doi.org/10.3934/mine.2022023 doi: 10.3934/mine.2022023 |
[16] | R. P. Feynman, R. Leighton, M. Sands, The Feynman lectures on physics, Volume I, 2015. |
[17] | F. Flandoli, E. Luongo, Heat diffusion in a channel under white noise modeling of turbulence, Mathematics in Engineering, 4 (2022), 1–21. http://doi.org/10.3934/mine.2022034 doi: 10.3934/mine.2022034 |
[18] | L. E. Hientzsch, On the low Mach number limit for 2D Navier–Stokes–Korteweg systems, Mathematics in Engineering, 5 (2023), 1–26. http://doi.org/10.3934/mine.2023023 doi: 10.3934/mine.2023023 |
[19] | J. Lukkarinen, H. Spohn, Weakly nonlinear Schrödinger equation with random initial data, Invent. Math., 183 (2011), 79–188. http://doi.org/10.1007/s00222-010-0276-5 doi: 10.1007/s00222-010-0276-5 |
[20] | S. Nazarenko, Wave turbulence, Berlin, Heidelberg: Springer, 2011. http://doi.org/10.1007/978-3-642-15942-8 |
[21] | C. Nobili, The role of boundary conditions in scaling laws for turbulent heat transport, Mathematics in Engineering, 5 (2023), 1–41. http://doi.org/10.3934/mine.2023013 doi: 10.3934/mine.2023013 |
[22] | A. Nota, J. J. L. Velázquez, Homoenergetic solutions of the Boltzmann equation: the case of simple-shear deformations, Mathematics in Engineering, 5 (2023), 1–25. http://doi.org/10.3934/mine.2023019 doi: 10.3934/mine.2023019 |
[23] | D. Varma, M. Mathur, T. Dauxois, Instabilities in internal gravity waves, Mathematics in Engineering, 5 (2023), 1–34. http://doi.org/10.3934/mine.2023016 doi: 10.3934/mine.2023016 |