STRICHARTS ESTIMATE FOR THE HIGHER DIMENSIONAL SCALAR FIELD EQUATION WITH NON MINIMAL COUPLING
In this paper we construct Strichartz estimate for the higher dimensional scalar field equation in the background of conformally flat space-time with non minimal coupling where the coupling interaction of the scalar field is proportional to the scalar curvature of the spacetime. The equation of...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/45711 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this paper we construct Strichartz estimate for the higher dimensional scalar
field equation in the background of conformally flat space-time with non minimal
coupling where the coupling interaction of the scalar field is proportional to the
scalar curvature of the spacetime. The equation of motion has the form like non linear
wave equation. We split the estimate into homogeneous and non homogeneous
part. Furthermore, we make the generalization to prove the existence of solutions
on complete Riemannian manifold with Ricci curvature bounded from below and
positive injectivity radius using energy estimate method. We have show that both
the kth-linear energy and energy norm are bounded for the finite time with the initial
data in Hk+1 Hk. We also have prove the uniqueness and smoothness properties
of the solutions. |
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