Blood pressure decreases as one stands up.
A model of cerebral blood flow has been created in Modeling Cerebral Blood Flow Control During Posture
Change From Sitting to Standing:
The characteristic features are that after standing up for 60 s, the pressure (both systolic and diastolic values) drops signiﬁcantly from a mean pressure of approximately 95 mmHg to a mean pressure of approximately 58 mmHg. At the same time, the blood ﬂow velocity also decreases followed by an increase. However, it should be noted that while the mean velocity decreases, the decrease is not as big, because of a large widening of the pulse-amplitude (systolic value minus diastolic value).
Other studies back this claim up such as Cerebral Circulation In Various Physologic States:
Although our studies have not revealed a quantitative relationship between alterations in the arterial pressure and cerebral blood flow in the same
person, there was a definite fall in cerebral blood
flow with the fall in effective cerebral arterial
pressure on standing.
More specific studies on posture and blood flow have also been performed to learn how to the best way to reduce blood pressure, which is important in head injury patients.
From Effect of head elevation on intracranial pressure, cerebral perfusion pressure, and cerebral blood flow in head-injured patients:
There was no statistically significant change in CPP, CBF, cerebral metabolic rate of oxygen, arteriovenous difference of lactate, or cerebrovascular resistance associated with the change in head position. The data indicate that head elevation to 30° significantly reduced ICP in the majority of the 22 patients without reducing CPP or CBF.
This means that Inter-Cranial Pressure (ICP) was significantly reduced in most patients without reducing Cerebral Blood Flow (CBF). This means changes in pressure do not always equate to changes in blood flow of the same relative magnitude.
Reading more into those articles will give you more insight into the complexities of how the flow changes in posture, but unless you have a more specific question I believe that covers what you asked.