The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations

202 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum (2012, background): “This type of inequality arises in a natural way in the analysis of quasilinear hyperbolic systems (see for instance [8]), and can be viewed as a generalization of standard nonlinear Gronwall inequalities.”
Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum (2009, methodology): “In order to obtain estimates independent of a regularization parameter κ defined in Section 4, we will also need the following Lemma, whose proof can be found in Lemma 1, Section 6 of [3]: Lemma 3.”
Well-posedness of the free-surface incompressible Euler equations with or without surface tension (2005, background): “We will then prove that this continuous in time energy is controlled by the same type of polynomial law as (41) of [7], which will provide a control independent of κ on a time independent of κ.”