Stability of Multidimensional Shocks

By G. Métivier. 2001

159 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f07a152a334651c7e9d1b4c6b772060dcd7cf61b

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations (2003, result): “These result have since been significantly sharpened and extended by Métivier and coworkers; see [Mé.5], and references therein.”
Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems (2005, methodology): “We first recall from [Mok], [Mé1] (see also [Mé2]) the handbook of results about the homogeneous paradifferential calculus with parameter, to be used in the hyperbolic regime.”
Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum (2009, unknown): “The stability and regularity of the multi-D shock solution was initiated in [29] and extensively studied by [13], [14], [15], and [32] (see the references in these articles for a more extensive bibliography).”
The Block Structure Condition for Symmetric Hyperbolic Systems (2000, background): “As a corollary, continuing the analysis as in [2], [1], [5] or [3], this implies the local well-posedness of boundary value problems for linear symmetric (or symmetrizable) hyperbolic systems of constant multiplicity which satisfy the uniform Lopatinski condition.”
Para-Differential Calculus and Applications to the Cauchy Problem for Nonlinear Systems (2008, unknown): “Bony [Bon] (see also [Mey], [Hör], [Tay], [Mé1]).”
The Existence of Current-Vortex Sheets in Ideal Compressible Magnetohydrodynamics (2009, methodology): “In this paper, to avoid assumptions about compact support of the initial data in the nonlinear existence theorem and work globally in R3+ we use the choice similar to that suggested by M´etivier [ 25 ]: (t,x) := x1 + (x1)f(t,x0),”