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We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
The Yang–Mills flow on a Kahler surface with holomorphic initial data converges smoothly away from a singular set determined by the Harder–Narasimhan–Seshadri filtration of the initial holomorphic bun...
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study o...
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation. We then present two global existence results for strong solutions to the equation. We finally obtain several b...
Abstract: In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for $p$-Laplacian, has finite time blow-up solutions.
Abstract: We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is al...
Abstract: Radial blow-up, including inhomogeneous versions, of boundary faces of a manifold (always with corners) is an important tool for resolving singularities, degeneracies and competing notions o...
Abstract: It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid boundary is given by Petrovskii's ...
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
Abstract: We extend an argument of Stoppa to make some prgress towards a proof that K\"ahler-Einstein manifolds are "b-stable". We point out some algebro-geometric questions, involving finite generati...
Abstract: We mainly discuss the Wu classes $v(M)$ and the Steenrod operation $Sq$ of the topological blow up $\tilde{M}$. The formula of the Wu class $v(\tilde{M})$ will be given as well as the formul...
In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that...
Given a symplectic manifold (M; !) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L.
This paper is concerned with blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system. We first derive precise blow-up scenarios for strong solutions to the system. The...
This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The exist...

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