Integral equations for the problem of stationary waves ... - Springer Link

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of free fall, Ix[ 2 = x~ + x~, and v0 is the unique positive root ... The method of integral equations has not been studied as well for problem (1.2)-(1.6). We briefly ...
INTEGRAL EQUATIONS FOR THE PROBLEM OF STATIONARY WAVES PRODUCED BY A FLOATING BODY N. G. Kuznetsov

I,

Suppose that an ideal incompressible heavy fluid fills a region

(x, y): y < 0 ,

x = (xl,x2)~R~}.

the following non-intersecting i)

W CR[

If its depth is infinite then the boundary

= {P =

0Wconsists

of

sets.

The moistened surface S of a body that is partially submerged in the fluid and

that fills a bounded simply connected region D in R ~ such that D ~ OR[ nected two-dimensional region. 2)

The free fluid surface

3)

The bottom

is a simply con-

Here S = OD N R~. F = aR[ ~ D.

B = {PER[:

y = --h}, where h > 0.

In the case of infinite depth we can assume that h = ~. We assume that the surface 8D belongs to the class C 2 and for every point of P contained in the water line

OR[.

the tangent surface to 3D is not equal to 3R~.

Then

O 0 the potential Vu has a finite Dirichlet integral over a cylindrical region {Ix l