Non-uniqueness of Admissible Solutions for the 2D Euler Equation with Vortex Data
F Mengual - Communications in Mathematical Physics, 2024 - Springer
For any 2< p<∞ we prove that there exists an initial velocity field v∘∈ L 2 with vorticity ω∘∈
L 1∩ L p for which there are infinitely many bounded admissible solutions v∈ C t L 2 to the …
L 1∩ L p for which there are infinitely many bounded admissible solutions v∈ C t L 2 to the …
Dissipative Euler flows originating from circular vortex filaments
F Gancedo, A Hidalgo-Torné, F Mengual - arXiv preprint arXiv:2404.04250, 2024 - arxiv.org
In this paper, we prove the first existence result of weak solutions to the 3D Euler equation
with initial vorticity concentrated in a circle and velocity field in $ C ([0, T], L^{2^-}) $. The …
with initial vorticity concentrated in a circle and velocity field in $ C ([0, T], L^{2^-}) $. The …
Entropy solutions to macroscopic IPM
Á Castro, D Faraco, B Gebhard - arXiv preprint arXiv:2309.03637, 2023 - arxiv.org
We investigate maximal potential energy dissipation as a selection criterion for subsolutions
(coarse grained solutions) in the setting of the unstable Muskat problem. We show that both …
(coarse grained solutions) in the setting of the unstable Muskat problem. We show that both …
On the energy-constrained optimal mixing problem for one-dimensional initial configurations
B Gebhard - arXiv preprint arXiv:2409.16886, 2024 - arxiv.org
We consider the problem of mixing a passive scalar in a periodic box by incompressible
vector fields subject to a fixed energy constraint. In that setting a lower bound for the time in …
vector fields subject to a fixed energy constraint. In that setting a lower bound for the time in …