Extension of the pole decomposition for the multidimensional Burgers equation.
It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity nu and no force are of the form u=-2nu inverted Delta ln P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such solutions have pole singularities on the complex algebraic varieties.
Frisch
U
U
CNRS, Observatoire de la Côte d'Azur, Nice, France.
Mineev-Weinstein
M
M