61 citations · 151 across the 9 of their papers we have counts for
14 papers
Nonlinear stability and existence of two-dimensional compressible current-vortex sheets
Alessandro Morando, Paolo Secchi, Paola Trebeschi +1
We are concerned with nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-…
Stability of an incompressible plasma-vacuum interface with displacement current in vacuum
Alessandro Morando, Paolo Secchi, Yuri Trakhinin +1
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys t…
Structural stability of shock waves in 2D compressible elastodynamics
Alessandro Morando, Yuri Trakhinin, Paola Trebeschi
We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic fluid in the sense of the local-in-time existence and uniqueness of d…
Two-Dimensional Vortex Sheets for the Nonisentropic Euler Equations: Nonlinear Stability
Alessandro Morando, Paola Trebeschi, Tao Wang
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear s…
On the evolution equation of compressible vortex sheets
Alessandro Morando, Paolo Secchi, Paola Trebeschi
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients we derive…
Local existence of MHD contact discontinuities
Alessandro Morando, Yuri Trakhinin, Paola Trebeschi
We prove the local-in-time existence of solutions with a contact discontinuity of the equations of ideal compressible magnetohydrodynamics (MHD) for 2D planar flows provided that t…
Data dependence of approximate current-vortex sheets near the onset of instability
Alessandro Morando, Paolo Secchi, Paola Trebeschi
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized st…
Existence of approximate current-vortex sheets near the onset of instability
Alessandro Morando, Paolo Secchi, Paola Trebeschi
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized st…
Approximate current-vortex sheets near the onset of instability
Alessandro Morando, Paolo Secchi, Paola Trebeschi
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized st…
Well-posedness of the linearized problem for contact MHD discontinuities
Alessandro Morando, Yuri Trakhinin, Paola Trebeschi
We study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics (MHD). They are characteristic discontinuities with no flow across the dis…
Characteristic boundary value problems: estimates from H1 to L2
Alessandro Morando, Paolo Secchi, Paola Trebeschi
Motivated by the study of certain non linear free-boundary value problems for hyperbolic systems of partial differential equations arising in Magneto-Hydrodynamics, in this paper w…
Well-posedness of the linearized plasma-vacuum interface problem
Paolo Secchi, Yuri Trakhinin
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compr…
A priori estimates for 3D incompressible current-vortex sheets
Jean-Francois Coulombel, Alessandro Morando, Paolo Secchi +1
We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutral…
A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems
Alessandro Giacomini, Paola Trebeschi
We prove that if $\Om \subseteq \R^2$ is bounded and $\R^2 \setminus \Om$ satisfies suitable structural assumptions (for example it has a countable number of connected components),…