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It is shown that the nonstationary Navier-Stokes equation (NS) in ℝ+×ℝ
is well posed in certain Morrey spacesM
) (see the text for the definition: in particularM
1,0 is the space of finite measures), in the following sense. Given a vectora∈M
p,m-p with diva=0...
The trouble with Newton's method for finding the roots of a complex polynomial is knowing where to start the iteration. In this paper we apply the theory of rational maps and some estimates based on distortion theorems for univalent functions to find lower bounds, depending only on the degreed,...
For anyb>0, there are dissipative analytic vector fields on ℝ2 which, when restricted to ℝ×(−b,b), have positive Jacobian and infinitely many (attracting) singularities.
We consider one-parameter families of two-dimensional diffeomorphisms with homoclinic tangencies. Various authors considered the dynamical complexities due to such tangencies satisfying certain nondegeneracy conditions. In this paper we provide methods to actually verify, for real analytic...
One proves the existence of a common zero for any two ℝ-analytic commuting vector fields on a 4-dimensional manifold with not zero Euler characteristic. A local version of this result remains true on 3-manifolds.
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