Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive estimates for linearized water wave type equations in
  $\mathbb R^d$   We derive a $L^1_x (\mathbb R^d)-L^{\infty}_x ( \mathbb R^d)$ decay estimate
of order $\mathcal O \left( t^{-d/2}\right)$ for the linear propagators $$\exp
\left( {\pm it \sqrt{ |D|\left(1+ \beta |D|^2\right) \tanh |D | } }\right),
\qquad \beta \in \{0, 1\}. \quad D = -i\nabla,$$ with a loss of $3d/4$ or
$d/4$-derivatives in the case $\beta=0$ or $\beta=1$, respectively. These
linear propagators are known to be associated with the linearized water wave
equations, where the parameter $\beta$ measures surface tension effects. As an
application we prove low regularity well-posedness for a Whitham-Boussinesq
type system in $\mathbb R^d$, $d\ge 2$. This generalizes a recent result by
Dinvay, Selberg and the third author where they proved low regularity
well-posedness in $\mathbb R$ and $\mathbb R^2$.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas