相关论文: Singularity and Mesh Divergence of Inviscid Adjoin…

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…

We study stationary homogeneous solutions to the 3D Euler equation. The problem is motivated be recent exclusions of self-similar blowup for Euler and its relation to Onsager conjecture and intermittency. We reveal several new classes of…

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…

We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…

Linear shear flow bounded by a plane wall is an idealization that occurs in microfluidic devices and many other applications. Perfect plane approximation neglects surface irregularities and discrete particles adsorbed at the surface. Here…

Maxwell's equations applied to a superconducting wire (aluminum) covered with a thick nonsuperconducting sheath (copper), in combination with the superfluid velocity equation for Cooper pairs which obeys DeWitt's minimal coupling rule,…

In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity…

We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a…

We show that certain singular structures (H\"{o}lderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure of these singularities is related to the modulus of…

We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by…

We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…

The reported spatial variation in the fine-structure constant at high redshift, if physical, could be due to the presence of dilatonic domains, and one or more domain walls inside our horizon. An absorption spectrum of an object in a…

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also…

We consider multi-dimensional junction problems for first- and second-order pde with Kirchoff-type Neumann boundary conditions and we show that their generalized viscosity solutions are unique. It follows that any viscosity-type…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

The process of collision of two parallel domain walls in a supersymmetric model is studied both in effective Lagrangian approximation and by numerical solving of the exact classical field problem. For small initial velocities we find that…

A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

We study the uniqueness of solutions with a transonic shock in a duct in a class of transonic shock solutions, which are not necessarily small perturbations of the background solution, for steady potential flow. We prove that, for given…