Nodal domain theorems à la Courant.
Nodal domains and spectral minimal partitions
Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains.
Non blow-up of the 3D ideal magnetohydrodynamics equations for a class of three-dimensional initial data in cylindrical domains.
Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
Non holonomie dans un problème de diffraction
Non prolongement unique des solutions d'opérateurs «somme de carrés»
Dans ce travail, nous avons montré que si , où les sont des champs de vecteurs linéairement independants dans un ouvert de tels que l’algèbre de Lie qu’ils engendrent soit de rang maximum en tout point et la forme volume qu’on leur associe soit de classe 4 en un point de , alors il existe un voisinage ouvert de et une fonction tels que possède pas la propriété de prolongement unique.
Nonanalytic solutions of the KdV equation.
Nonanalyticity of solutions to
It is proved that the solution to the initial value problem , u(0,x) = 1/(1+x²), does not belong to the Gevrey class in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems
We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force . We assume that is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if is a quasiperiodic function with respect to , then the attractor is a continuous image of a torus. Moreover the...
Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems
We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g(x,t). We assume that g(x,t) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g(x,t) is a quasiperiodic function with respect to t, then the attractor is a continuous image...
Nonexistence and radial symmetry of positive solutions of semilinear elliptic systems.
Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type.
Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations
Nonexistence of entire positive solution for a conformal -Hessian inequality
In this paper, we study the nonexistence of entire positive solution for a conformal -Hessian inequality in via the method of proof by contradiction.
Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid
We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on . To prove these results, some new average quantities are...
Nonexistence of global solutions of nonlinear wave equations.
Nonexistence of minimal blow-up solutions of equations in
Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
Nonexistence of positive solution for quasilinear elliptic problems in the half-space.