SDLThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.https://preprints.sissa.it:443/xmlui2018-10-31T17:26:08Z2018-10-31T17:26:08ZCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equationsBianchini, StefanoSpinolo, Laurahttp://preprints.sissa.it/handle/1963/353252018-10-17T00:00:27Z2018-10-16T00:00:00ZCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations
Bianchini, Stefano; Spinolo, Laura
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the
mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.
2018-10-16T00:00:00ZOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)Tasso, Emanuelehttp://preprints.sissa.it/handle/1963/353242018-09-25T00:00:25Z2018-09-01T00:00:00ZOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)
Tasso, Emanuele
In this paper we present a new result of continuity for the trace operator acting on
functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis
of being rectifiable and of finite measure. We also show an application of our result in relation
to the variational model of elasticity with cracks, when the associated minimum problems are
coupled with Dirichlet and Neumann boundary conditions.
27 pages
2018-09-01T00:00:00ZNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysisMichelangeli, AlessandroPitton, Giuseppehttp://preprints.sissa.it/handle/1963/353232018-09-21T00:00:25Z2018-09-01T00:00:00ZNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis
Michelangeli, Alessandro; Pitton, Giuseppe
We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.
2018-09-01T00:00:00ZOn Geometric Quantum Confinement in Grushin-Like ManifoldsGallone, MatteoMichelangeli, AlessandroPozzoli, Eugeniohttp://preprints.sissa.it/handle/1963/353222018-09-20T00:00:27Z2018-09-01T00:00:00ZOn Geometric Quantum Confinement in Grushin-Like Manifolds
Gallone, Matteo; Michelangeli, Alessandro; Pozzoli, Eugenio
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.
16 pages
2018-09-01T00:00:00Z