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Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity
The existence of two-dimensional standing waves on the surface of an infinitely deep perfect fluid under gravity is established. When formulated as a second-order equation for a real-valued functionExpand
Nash-Moser Theory for Standing Water Waves
Abstract We consider a perfect fluid in periodic motion between parallel vertical walls, above a horizontal bottom and beneath a free boundary at constant atmospheric pressure. Gravity actsExpand
Modelling nonlinear hydroelastic waves
This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff’s hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and anExpand
Convexity of Stokes Waves of Extreme Form
Existence is established of a piecewise-convex, periodic, planar curve S below which is defined a harmonic function which simultaneously satisfies prescribed Dirichlet and Neumann boundary conditionsExpand
NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS
The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem hasExpand
Small Divisor Problem in the Theory of Three-dimensional Water Gravity Waves
We consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity g and resulting from the nonlinear interaction of two simply periodicExpand
Boundary value problems for transport equations
The first order scalar differential equation \( {\rm \mathbf{u}} . \nabla \varphi + b\varphi = f ,\) which is called the transport equation, is one of the basic equations of mathematical physics. ItExpand
A Proof of the Stokes Conjecture in the Theory of Surface Waves
This article gives a proof of the famous Stokes conjecture that a gravity wave of greatest height on water has a corner with contained angle 2π/3 at its singular point.
Inhomogeneous boundary value problems for compressible Navier–Stokes and transport equations☆
Abstract In the paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. The well-posedness for inhomogeneous boundary valueExpand
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
TLDR
We prove the existence, uniqueness and shape differentiability of solutions to inhomogeneous boundary value problems for compressible Navier-Stokes equations of elliptic-hyperbolic type. Expand
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