On continuity properties of solution maps of the generalized SQG family

Hydrology, hydrography, oceanography (86A05) Applications of Lie (super)algebras to physics, etc. (17B81) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) PDEs in connection with geophysics (35Q86) Euler equations (35Q31)

Cites Work

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The SQG equation as a geodesic equation
Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations
On the regularity of the solution map of the incompressible Euler equation
Nonlinear evolution equations and the Euler flow
Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics
On nonstationary flows of viscous and ideal fluids in $L^ p_ s({\mathbb{R}}^ 2)$
Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations
Remarks on well-posedness of the generalized surface quasi-geostrophic equation
On the ill-posedness of some canonical dispersive equations.
Classical solutions of the periodic Camassa-Holm equation.
Holomorphic structures with weak spatial regularity in fluid mechanics
Galilean boost and non-uniform continuity for incompressible Euler
Non-uniform dependence for Euler equations in Besov spaces
On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces
On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces
Groups of diffeomorphisms and the motion of an incompressible fluid
Fredholm properties of Riemannian exponential maps on diffeomorphism groups
Generalized surface quasi-geostrophic equations with singular velocities
On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
Nonuniform Dependence on Initial Data for Compressible Gas Dynamics: The Cauchy Problem on $\mathbb{R}^2$
Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces
On the Ill-Posedness of the IVP for the Generalized Korteweg-De Vries and Nonlinear Schrödinger Equations

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