64 citations · 78 across the 12 of their papers we have counts for
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Lifespan Bounds and Super-Classical Propagation for Weak Solutions of the Three-Dimensional Compressible Euler Equations
Thomas C. Sideris
We establish an upper bound on the lifespan of bounded weak solutions to the three-dimensional isentropic compressible Euler equations on , under a localize…
Expansion and collapse of spherically symmetric isotropic elastic bodies surrounded by vacuum
Thomas C. Sideris
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes in…
Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D
Boyan Jonov, Paul Kessenich, Thomas C. Sideris
The initial value problem for Hookean incompressible viscoelastictic motion in three space dimensions has global strong solutions with small displacements.
Affine motion of 2d incompressible fluids surrounded by vacuum and flows in
Jay Roberts, Steve Shkoller, Thomas C. Sideris
The affine motion of two-dimensional (2d) incompressible fluids surrounded by vacuum can be reduced to a completely integrable and globally solvable Hamiltonian system of ordinary…
Global existence of near-affine solutions to the compressible Euler equations
Steve Shkoller, Thomas C. Sideris
We establish global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into vacuum. Vacuum states can occur with eith…
Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons
Felipe Linares, Gustavo Ponce, Thomas C. Sideris
We study special properties of solutions to the IVP associated to the Camassa-Holm equation on the line related to the regularity and the decay of solutions. The first aim is to sh…
Global existence and asymptotic behavior of affine motion of 3D ideal fluids surrounded by vacuum
Thomas C. Sideris
The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system…
Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics
Zhen Lei, Thomas C. Sideris, Yi Zhou
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval , for initial data of th…
Stability in of circular vortex patches
Thomas C. Sideris, Luis Vega
The motion of incompressible and ideal fluids is studied in the plane. The stability in of circular vortex patches is established among the class of all bounded vortex patche…
Global Existence for Systems of Nonlinear Wave Equations in 3D with Multiple Speeds
Thomas C. Sideris, Shu-Yi Tu
Global smooth solutions to the initial value problem for systems of nonlinear wave equations with multiple propagation speeds will be constructed in the case of small initial data…
Nonresonance and global existence of prestressed nonlinear elastic waves
Thomas C. Sideris
The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an addi…