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- Centre National de la Recherche ScientifiqueFR214 papers
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11 papers · 2 filters
Well-posedness for KdV-type equations with quadratic nonlinearity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of the KdV-type equation \[ \partial_t u + \frac{1}{3} \partial_x^3 u = c_1 u \partial_x^2u + c_2 (\partial_x u)^2, \quad u(0)=u_0. \] Pilod (2008) s…
Biharmonic wave maps into spheres
Sebastian Herr, Tobias Lamm, Roland Schnaubelt
A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved b…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (200…
Nonlocal quadratic forms with visibility constraint
Moritz Kassmann, Vanja Wagner
Given a subset of the Euclidean space, we study nonlocal quadratic forms that take into account tuples if and only if the line segment between and $y…
On shorttime bilinear Strichartz estimates and applications to improve the energy method
Robert Schippa
A refinement of the energy method is introduced for dispersive PDE with derivative nonlinearity posed on tori. Key ingredient is a shorttime bilinear Strichartz estimate, which is…
Determinstic and stochastic 2d Navier-Stokes equations with anisotropic viscosity
Siyu Liang, Ping Zhang, Rongchan Zhu
In this paper, we investigate both deterministic and stochastic 2D Navier Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posednes…