Analysis and ApplicationsAccepted Papers No AccessSubsonic flows with a contact discontinuity in two-dimensional finitely long curved nozzleShangkun Weng Zihao ZhangShangkun Zhanghttps://orcid.org/0000-0003-0370-1243 Search for more papers by this author https://doi.org/10.1142/S0219530525500095Cited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend Library ShareShare onFacebookTwitterLinked...

This paper concerns the structural stability of subsonic flows with a contact discontinuity in finitely long axisymmetric cylinder. We establish existence and uniqueness by prescribing horizontal mass flux distribution, swirl velocity, entropy Bernoulli’s quantity at entrance radial velocity exit. It can be formulated as free boundary problem to determined simultaneously flows. Compared two-dimensional case, new difficulty arises due singularity near axis. An invertible modified Lagrangian...

We concern the structural stability of supersonic flows with a contact discontinuity in finitely long curved nozzle for two‐dimensional steady compressible rotating Euler system. Concerning effect Coriolis force, we first establish existence shear flat nozzle. then investigate these background under perturbations incoming flow and upper lower walls. It can be formulated as an initial boundary value problem free boundary. The Lagrangian transformation is employed to straighten fix...

We concern the structural stability of transonic shocks for steady Euler system with an external force in axisymmetric perturbed cylinder. For a class forces, we first prove existence and uniqueness shock solution to one-dimensional force, which shows that has stabilization effect on flat cylinder position is uniquely determined. then establish under perturbations incoming supersonic flow, nozzle boundary, exit pressure force. Different from problem two-dimensional nozzles, there exists...

We establish the existence and uniqueness of transonic shock solution for steady isentropic Euler system with an external force in a rectangular cylinder under three-dimensional perturbations incoming supersonic flow, exit pressure force.The has stabilization effect on shocks flat nozzles is completely free, we do not require it passing through fixed point.By utilizing deformation-curl decomposition to decouple hyperbolic elliptic modes effectively reformulating Rankine-Hugoniot conditions,...

In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence uniqueness of the flow are obtained via variational formulation. optimal decay rate at far fields is also derived by Kelvin's transformation some elliptic estimates. By extracting solutions as approximate sequences, obtain limit solution. main ingredients our analysis methods calculus variations, theory second-order quasilinear equations compactness framework.

This paper concerns the structural stability of supersonic flows with a contact discontinuity in finitely long curved nozzle for two-dimensional steady compressible rotating Euler system. Concerning effect Coriolis force, we first establish existence shear flat nozzle. Then consider these background when incoming flow and upper lower walls are suitably perturbed. The problem can be formulated as an initial boundary value free boundary. To deal problem, Lagrangian transformation is introduced...

This paper concerns the structural stability of subsonic flows with a contact discontinuity in finitely long axisymmetric cylinder. We establish existence and uniqueness by prescribing horizontal mass flux distribution, swirl velocity, entropy Bernoulli's quantity at entrance radial velocity exit. It can be formulated as free boundary problem to determined simultaneously flows. Compared two-dimensional case, new difficulty arises due singularity near axis. One key points analysis is...

We establish the existence and uniqueness of transonic shock solution for steady isentropic Euler system with an external force in a rectangular cylinder under three-dimensional perturbations incoming supersonic flow, exit pressure force. The has stabilization effect on shocks flat nozzles is completely free, we do not require it passing through fixed point. By utilizing deformation-curl decomposition to decouple hyperbolic elliptic modes effectively reformulating Rankine-Hugoniot...

We find by applying MacMahon's partition analysis that all magic labellings of the cube are eight types, each generated six basis elements. A combinatorial proof this fact is given. The number thus reobtained as a polynomial in sum degree $5$. Then we enumerate distinct labellings, which turns out to be quasi-polynomial period 720720. also group symmetry can used significantly simplify computation.

For any integer $m\geq 2$ and $r \in \{1,\dots, m\}$, let $f_n^{m,r}$ denote the number of $n$-Dyck paths whose peak's heights are $im+r$ for some $i$. We find generating function satisfies a simple algebraic functional equation degree $2$. The $r=m$ case is particularly nice we give combinatorial proof. By using Sulanke Xin's continued fraction method, calculate Hankel determinants $f_n^{m,r}$. special our result solves conjecture proposed by Chien, Eu Fu. also enriched class eventually...