41 citations · 105 across the 14 of their papers we have counts for
11 papers · 1 filter
Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation
Giacomo Del Nin, Daniel Faraco, Sauli Lindberg +1
For any smooth bounded domain , we construct a divergence-free velocity field for all , and magnetic fields $B^ε\in L_t^…
On the integrability properties of Leray-Hopf solutions of the Navier-Stokes equations on
Sauli Lindberg
Let and consider the Navier-Stokes equations on . We study the following two questions for suitable -homogeneous Banach spaces $X \subset \mat…
Relaxation of the kinematic dynamo equations
Lauri Hitruhin, Sauli Lindberg
We compute the exact relaxation and -convex hull of the kinematic dynamo equations and show that they coincide. We also find the relaxation in the stationary case.
Magnetic helicity, weak solutions and relaxation of ideal MHD
Daniel Faraco, Sauli Lindberg, László Székelyhidi
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed…
Energy minimisers with prescribed Jacobian
André Guerra, Lukas Koch, Sauli Lindberg
We study the symmetry and uniqueness of maps which minimise the -Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function . We find…
Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs
André Guerra, Lukas Koch, Sauli Lindberg
For a nonlinear operator satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) is surjective, ii) is open at z…
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
André Guerra, Lukas Koch, Sauli Lindberg
We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, , where is integrable and bounded away from zero. In…
The lamination convex hull of stationary IPM
Lauri Hitruhin, Sauli Lindberg
We compute the lamination convex hull of the stationary IPM equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination conve…
Bounded solutions of ideal MHD with compact support in space-time
Daniel Faraco, Sauli Lindberg, László Székelyhidi
We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and…
Proof of Taylor's conjecture on magnetic helicity conservation
Daniel Faraco, Sauli Lindberg
We prove Taylor's conjecture which says that in 3D MHD, magnetic helicity is conserved in the ideal limit in bounded, simply connected, perfectly conducting domains. When the domai…
Magnetic helicity and subsolutions in ideal MHD
Daniel Faraco, Sauli Lindberg
We show that ideal 2D MHD does not possess weak solutions (or even subsolutions) with compact support in time and non-trivial magnetic field. We also show that the -convex hull…