Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 7 of 7 for “"Global regularity"”.
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Global Regularity for Euler Vortex Patch in Bounded Smooth Domains
… enough initially. In bounded domains, the regularity theory for patch solutions is less complete. In this thesis, I study the Euler vortex patch in a general smooth bounded domain. I prove global in time regularity by providing the upper bound of the growth on curvature of the patch …
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Diederich-Fornæss Index on Boundaries Containing Crescents
… domains that fails to satisfy global regularity of the Bergman Projection, due to the set of weakly pseudoconvex points that form an annulus in its boundary. We instead examine a bounded pseudoconvex domain Ω ⊂ C2 whose set of weakly pseudoconvex points form a crescent in its …
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Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
… of twisted Laplacians. They are proved to be globally hypoelliptic in the Schwartz space and in the Gelfand-Shilov spaces using the Green functions of the twisted Laplacians. Global regularity in a scale of Sobolev spaces of these twisted Laplacians is given. Equally important are the heat …
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Transport in Biology, from Theory to Application
… (CMV) with experimental data.Our methods include regularity estimates, maximal and comparison principles, probabilistic techniques, and stochastic processes. This work resulted in several conclusions: We prove quantitatively chemotaxis enhances reaction in 1D setting: the upper bound for reaction …
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Critical thresholds in Eulerian dynamics
In this thesis, we study the critical regularity phenomena in Eulerian dynamics, $u_t+u\cdot \nabla u=F(u,D u,\cdots), $ here $F$ represents a general force acting on the flow and by regularity we seek to obtain a large set of sub-critical initial data. We analyze three prototype models, ranging …
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Well-posedness and scattering of the Chern-Simons-Schrödinger system
The subject of the present thesis is the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in two spatial dimensions with a long-range electromagnetic field. The present thesis studies two aspects of the system: that of well-posedness and that of the long-time …
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Global normal forms and global properties in function spaces for second order Shubin type operators
We investigate the reduction to global normal forms of second order Shubin(or G) type differential operators P(x;D) in functional spaces on Rn. We describe the isomorphism properties of normal form transformations, introduced by L. Hormander for the study of affine symplectic transformations acting …