[HTML][HTML] Non existence and strong ill-posedness in Ck and Sobolev spaces for SQG
D Córdoba, L Martínez-Zoroa - Advances in Mathematics, 2022 - Elsevier
We construct solutions in R 2 with finite energy of the surface quasi-geostrophic equations
(SQG) that initially are in C k (k≥ 2) but that are not in C k for t> 0. We prove a similar result …
(SQG) that initially are in C k (k≥ 2) but that are not in C k for t> 0. We prove a similar result …
Non-existence and Strong lll-posedness in for the Generalized Surface Quasi-geostrophic Equation
D Córdoba, L Martínez-Zoroa - Communications in Mathematical Physics, 2024 - Springer
We consider solutions to the generalized Surface Quasi-geostrophic equation (γ-SQG) when
the velocity is more singular than the active scalar function (ie γ∈(0, 1)). In this paper we …
the velocity is more singular than the active scalar function (ie γ∈(0, 1)). In this paper we …
Strong illposedness for SQG in critical Sobolev spaces
We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed
in critical Sobolev spaces: there exists an initial data $ H^{2}(\bbT^ 2) $ without any solutions …
in critical Sobolev spaces: there exists an initial data $ H^{2}(\bbT^ 2) $ without any solutions …
Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation
Z Ye - Journal of Functional Analysis, 2022 - Elsevier
In this paper, we are concerned with the long-time asymptotic behavior of the generalized
two-dimensional quasi-geostrophic equation. More precisely, we obtain the sharp time …
two-dimensional quasi-geostrophic equation. More precisely, we obtain the sharp time …
On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces
MS Jolly, A Kumar, VR Martinez - Communications in Mathematical …, 2021 - Springer
This paper studies the dissipative generalized surface quasi-geostrophic equations in a
supercritical regime where the order of the dissipation is small relative to order of the …
supercritical regime where the order of the dissipation is small relative to order of the …
On well/ill-posedness for the generalized surface quasi-geostrophic equations in H\" older spaces
We establish the well/ill-posedness theories for the inviscid $\alpha $-surface quasi-
geostrophic ($\alpha $-SQG) equations in H\" older spaces, where $\alpha= 0$ and …
geostrophic ($\alpha $-SQG) equations in H\" older spaces, where $\alpha= 0$ and …
On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces
A Kumar, VR Martinez - arXiv preprint arXiv:2309.05844, 2023 - arxiv.org
This paper considers a family of active scalar equations which modify the generalized
surface quasi-geostrophic (gSQG) equations through its constitutive law or dissipative …
surface quasi-geostrophic (gSQG) equations through its constitutive law or dissipative …
Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex
D Cobb, M Donati, L Godard-Cadillac - arXiv preprint arXiv:2401.02728, 2024 - arxiv.org
This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with
parameter 0< s< 1. We obtained local existence of classical solutions in H^ 4 under the …
parameter 0< s< 1. We obtained local existence of classical solutions in H^ 4 under the …
[PDF][PDF] Non-existence, strong ill-posedness and loss of regularity for active scalar equations
LM Zoroa - 2023 - icmat.es
In this thesis we study the behaviour of several active scalar equations in spaces where
wellposedness is not expected, namely we study 2D-Euler, the Surface Quasi-Geostrophic …
wellposedness is not expected, namely we study 2D-Euler, the Surface Quasi-Geostrophic …
[图书][B] On Well-Posedness of Generalized Surface Quasi-Geostrophic Equations in Critical Sobolev Spaces
A Kumar - 2022 - search.proquest.com
The generalized surface quasi-geostrophic equations (gSQG) is a family of active scalar
transport equations that interpolates between the 2D incompressible Euler equation and the …
transport equations that interpolates between the 2D incompressible Euler equation and the …