69 citations · 258 across the 25 of their papers we have counts for
26 papers
Three-dimensional structural stability of shock waves in elastodynamics
Artem Shafeev, Yuri Trakhinin
We study the three-dimensional structural stability of shock waves for the equations of elastodynamics governing isentropic flows of compressible inviscid elastic materials. By non…
Stabilizing effect of surface tension for the linearized MHD-Maxwell free interface problem
Yuri Trakhinin
We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible…
Well-posedness for moving interfaces in anisotropic plasmas
Yuri Trakhinin
We study the local-in-time well-posedness for an interface that separates an anisotropic plasma from a vacuum. The plasma flow is governed by the ideal Chew-Goldberger-Low (CGL) eq…
Well-posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD
Yuri Trakhinin, Tao Wang
We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equati…
Nonlinear Stability of MHD Contact Discontinuities with Surface Tension
Yuri Trakhinin, Tao Wang
We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface te…
Well-Posedness for the Free-Boundary Ideal Compressible Magnetohydrodynamic Equations with Surface Tension
Yuri Trakhinin, Tao Wang
We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions…
On weak stability of shock waves in 2D compressible elastodynamics
Yuri Trakhinin
By using an equivalent form of the uniform Lopatinski condition for 1-shocks, we prove that the stability condition found by the energy method in [A. Morando, Y. Trakhinin, P. Treb…
Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics
Yuri Trakhinin
We study the free boundary problem for a contact discontinuity for the system of relativistic magnetohydrodynamics. A surface of contact discontinuity is a characteristic of this s…
Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics
Yuri Trakhinin, Tao Wang
We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vani…
Structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics
Yuri Trakhinin
We study the structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics (SMHD) in the sense of the local-in-time existence and uniqueness o…
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…
On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum
Yuri Trakhinin
In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-…
Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD
Lizhi Ruan, Yuri Trakhinin
We are concerned with a model of ideal compressible isentropic two-fluid magnetohydrodynamics (MHD). Introducing an entropy-like function, we reduce the equations of two-fluid MHD…
Elementary symmetrization of inviscid two-fluid flow equations giving a number of instant results
Lizhi Ruan, Yuri Trakhinin
We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two f…
Well-posedness of the free boundary problem in compressible elastodynamics
Yuri Trakhinin
We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the column…
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…
On well-posedness of the plasma-vacuum interface problem: the case of non-elliptic interface symbol
Yuri Trakhinin
We consider the plasma-vacuum interface problem in a classical statement when in the plasma region the flow is governed by the equations of ideal compressible magnetohydrodynamics,…
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…
Influence of vacuum electric field on the stability of a plasma-vacuum interface
Nikita Mandrik, Yuri Trakhinin
We study the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics. Unlike the classical statement, when the vacuum magnetic field obeys…
Well-posedness of the 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…
Symmetrizations of RMHD equations and stability of relativistic current-vortex sheets
Heinrich Freistühler, Yuri Trakhinin
We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equati…
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…
Stability of relativistic plasma-vacuum interfaces
Yuri Trakhinin
We study the plasma-vacuum interface problem in relativistic magnetohydrodynamics for the case when the plasma density does not go to zero continuously, but jumps. In the vacuum re…