@misc{9242933,
  abstract     = {{This thesis studies the analytic structure of steady two-dimensional water waves using methods from complex analysis. For incompressible, inviscid, irrotational flows, the velocity field can be described by a complex potential that is analytic in the fluid domain. This analytic structure allows the use of conformal mapping and analytic continuation techniques to study the geometry of the free surface and the behaviour of the flow beyond the physical fluid region. A central result discussed in this work is Lewy’s theorem on analytic continuation across free boundaries, which explains why steady water wave profiles are locally analytic away from stagnation points. Building on this framework, the thesis examines the appearance of singu- larities in analytically continued solutions following the analysis of Tanveer. In particular, singularities of square-root branch point type arise in the complex plane outside the physical domain and determine the radius of convergence of analytic representations of the free surface. The thesis also discusses the role of surface tension in the regularity and analytic continuation of water waves.}},
  author       = {{Bhattacharya, Arpita}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Singularities in Steady Water Waves Using Analytic Continuation}},
  year         = {{2026}},
}