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On the Cauchy Problem for Axi-Symmetric Vortex Rings
, 2013We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry.
Hao Feng, V. Sverák
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Cauchy Problem for Dissipative Hölder Solutions to the Incompressible Euler Equations
, 2013We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or Hölder continuous for any exponent $${\theta < \frac{1}{16 ...
S. Daneri
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Semilinear Cauchy problem [PDF]
, 1992 In this last chapter, we will state and prove a theorem of Lebeau [L4] giving a geometric upper bound for the wave front set of the solution of a semilinear wave equation with Cauchy data conormal along an analytic submanifold of the Cauchy hyperplane t = O.
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2013
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking.
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In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking.
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On The Cauchy Problem for Periodic KDV-Type Equations
, 2020J. Bourgain
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1970
Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data
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Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data
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The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation
, 2019Fan Yang, Pan Zhang, Xiao-xiao Li
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Navigating financial toxicity in patients with cancer: A multidisciplinary management approach
Ca-A Cancer Journal for Clinicians, 2022Grace Li Smith +2 more
exaly
Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation
Journal of Scientific Computing, 2016Yao Sun
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