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Local-in-time existence of a free-surface 3D Euler flow with H ^2+δ initial vorticity in a neighborhood of the free boundary

https://doi.org/10.1088/1361-6544/aca5e3

Kukavica, I; Ożański, W S (December 2022, Nonlinearity)

Abstract We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_{0} \in H^{2.5 + δ}$ is such that $c u r l u_{0} \in H^{2 + δ}$ in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition.
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Local existence of strong solutions to the stochastic Navier-Stokes equations with L data

https://doi.org/10.1016/j.jde.2023.02.021

Kukavica, Igor; Xu, Fanhui (June 2023, Journal of Differential Equations)

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Asymptotic properties of the Boussinesq equations with Dirichlet boundary conditions

https://doi.org/10.3934/dcds.2023040

Kukavica, Igor; Massatt, David; Ziane, Mohammed (January 2023, Discrete and Continuous Dynamical Systems)

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On quantitative uniqueness for parabolic equations

https://doi.org/10.1016/j.jde.2022.09.011

Kukavica, Igor; Le, Quinn (December 2022, Journal of Differential Equations)

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Global existence for the stochastic Navier–Stokes equations with small 𝐿𝑝 data

https://doi.org/s40072-021-00196-9

Igor Kukavica, Fanhui Xu (June 2022, Stochastics and partial differential equations)

We consider the stochastic Navier–Stokes equations in T^3 with multiplicative white noise. We construct a unique local strong solution with initial data in L^p, where p > 5. We also address the global existence of the solution when the initial data is small in L^p, with the same range of p.
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