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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2023 • Question 2

Question

Math 6510 • Differentiable Manifolds Spring 2023 • Question 2

Let \(V\) be a smooth vector field on \(\mathbb {R}^2\) and assume that outside of a

compact set \(V=\frac {\partial }{\partial x}\) where \(\frac {\partial }{\partial x}\) is the standard horizontal vector field. Show that the flow for \(V\) exists for all time.

Raw LaTeX

Let \(V\) be a smooth vector field on \(\mathbb{R}^2\) and assume that outside of a

compact set \(V=\frac{\partial}{\partial x}\) where \(\frac{\partial}{\partial x}\) is the standard horizontal vector field.
Show that the flow for \(V\) exists for all time.

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows